Jesus Christ is one divine person who took on human nature. If one says Christ is both a human person and a divine person this is a form of nestorianism. One person and two natures is the correct phraseology. His human nature was created, but he is not a human person. If His hypostasis is called "composite" after the Incarnation that is not because He is now a divine-human Person but because now there is, in His Person, two natures. So, its a composite hypostasis on the level of nature not in the level of hypostasis. The human nature is enhypostatized in Christ's hypostasis.
All Orthodox affirm with Chalcedon a single hypostasis. J.H. accepts no language other than divine-human hypostasis. That there is a composition in the hypostasis of Christ, there is no doubt: He is God and Man, passable and impassive, mortal and immortal, and so on, according to the attributes of both natures. The term "divine-human" - theantropikos, theandrikos - was used, among the Fathers, not in relation to the hypostasis, but in relation to theanthropic energies or activity.
J.H. later realized the confusion that his statement "[Jesus] is a human person" caused and then tried to clarify his previous post yet he continued to affirm that Christ is a divine-human hypostasis:
Let us take a look at what Fr. John Anthony McGuckin has to say in his book "Saint Cyril of Alexandria and the Christological Controversy":
In the text of the letter there is no direct reference to Constantinople or the Nestorian affair but it is undoubtedly in Cyril's mind for he uses the occasion to affirm the reality of the manhood of Christ but insists on the singleness of his divine personality—the classical and orthodox Alexandrian position from which he will not move an inch in all his subsequent theologising. In the Paschal Homily 17 he takes care to apply the title Meter Theou (a synonym of Theotokos) to demonstrate his point.
J.H.- and those who sided with him - affirmed precisely Nestorius' argument: every nature must be hypostatised:
On the corresponding semantic rules it followed that any real existent had to be hypostatised, and here opened up the real chasm between Cyril's way of thinking and that of Nestorius. The former saw that there could only be one hypostatic reality in Christ, if indeed Christ was to be one (though he meant hypostasis to bear the weight of subject-centre) whereas the latter followed the logical thread more rigidly and argued that every ousia had to be hypostatised separately. [...] Although Cyril would agree that all natures must be hypostatised he did not agree that this meant Christ must therefore have two hypostases. For him the whole point of the argument was that the two natures were not separate independent realities, and thus were both realised, in the one Christ, by one hypostasis. The use of mono-hypostatic language eventually won the day, but it took the next generation, at Chalcedon, to spell the argument out in the technical terms: Two natures (divine and human), one hypostasis (divine) in the one Christ.
Again, the Divine Hypostasis of the Word of God was the single personal subject:
Cyril uses hypostasis largely in the newer sense to describe the manner of the union in Christ. He says frequently, for example, that the union took place `Kath Hypostasin': hypostatically, or on the basis of a hypostatic level. What he means by this is to stress that the union of God and man in Christ is properly understood to have been effected precisely because it was a single individual subject (the hypostasis: God the Word) who realised the union of two different realities (divinity and humanity) by standing as the sole personal subject of both.
Again, J.H. used the same argument of Nestorius: Christ human nature must have its own hypostasis otherwise its not a real but only notional.
[Nestorius] studiously avoided using the form hypostasis to describe the christological union, in direct criticism of Cyril's preferred language. When Nestorius did speak of the term it was only to make two points: firstly that the word was highly 'physical' in its associated meanings and utterly inappropriate for use in the christology debate since it could suggest an organic or chemical model of union; and secondly that any ousia without a hypostasis of its own would, therefore, not be a real existent. The latter point was a significant attack on Cyril who had argued that Christ's humanity did not have a corresponding human hypostasis of its own (and thus Christ was not an individual man, rather God the Word enfleshed). Cyril saw this argument as crucial in defending the single subjectivity of the incarnate Lord; Nestorius attacked it on the logico-semantic grounds that if Christ's humanity did not have its own hypostasis then that humanity was only notional, not real. Whereas Nestorius demanded logical exactitude in the theological exchange, Cyril preferred to defend an intuited principle of single subjectivity regardless of the strains his varied use of technical terms placed on his hearers or upon logic itself.
Now, a excerpt of Fr. John Anthony McGuckin on Nestorius' Christology. Note the resemblance of his Christology and that promoted by J.H:
For Nestorius, the terms Christ, Son or Lord, were thus the correct titles to connote the faith experience of the oneness of the incarnate Saviour. These terms alone were the proper designation of the 'prosopon of union'—that observable phenomenon of the one reality of Christ in whom was also experienced the reality of a single human life (the prosopon of Jesus) and the very presence of the Godhead (the prosopon of the Logos); thus two realities.
Central to the coherence of Nestorius' thought was his belief that all christological thinking should always begin from this concrete experience the church has of Christ in his double reality. He felt that christology ought never to begin with the man Jesus (which would lead to Adoptionism) or with the divine Logos (which would lead to Docetism or Apollinarism). He complained, for example, that Cyril began the whole doctrinal process from the wrong premise and consequently deduced fallacious results:
"You start your account with the creator of the natures and not with the prosopon of union. It is not the Logos who has become two-fold, it is the one Lord Jesus Christ who is two-fold in his natures. In him are seen all the characteristics of the divine Logos who has an eternal, impassible, and immortal nature, and all the characteristics of the manhood which is mortal, passible, and created, and lastly those of the union and the incarnation."
To begin the christological process from any other starting point than the Christ who stands before the eyes of faith as God's unique statement of what the concrete realisation of 'divine' means is, for Nestorius, tantamount to disregarding the whole economy of salvation. But if one starts one's doctrine from Christ, he insists, then the principal lesson learned should be the sense of abiding distinctness in the one Christ's revelation of the divine, and his revelation of the human.
In so far as a prosopon signifies 'observable aspect' or 'communicable external appearance' then perhaps we can sum up Nestorius' position so far as follows: The eyes of faith recognise in Christ two clearly observed aspects of his reality, which signify to the beholder divinity as well as humanity. Christ, therefore, has two prosopa. At the same time the eyes of faith recognise that this Christ who has two prosopa is not the same as those prosopa themselves. In other words Christ is not the Logos as such. It would be bad theology, for Nestorius, to speak of the pre-existent Christ, since he is not eternal as the Logos is. Nor would it be right to make unqualified statements about the impassibility of Christ since the radical qualification of human limitations and sufferings is an integral part of what the mind understands by the word 'Christ'.
But in just the same way as the Logos is not synonymous with Christ, neither is the man Jesus of Nazareth. Christ, for Nestorius, was no mere man. The word connotes far more than the term 'the man Jesus'; in fact it connotes the whole mystery of the intimate relationship of this man with the divine Logos, and the union of the Logos with him. Christ is not only a word for the union of these two prosopic realities, it is also the concrete experience, in some way, of how that union has taken place, how it is to be conceived, and how it ought to be articulated by the church. The term Christ signifies the experience of the encounter with this unique composite figure of the Son of God. In the light of this it is not enough merely to insist that there are two prosopa in Christ, because the experience of the unique revelation of Christ calls for the confession that here there is also the `prosopon of union' the one Christ who manifests in a single prosopon (observable reality) the differentiated prosopa of the divine Logos, and the human Jesus. There are two prosopa, and there is one prosopon. This is why the starting point of one's consideration is all-important. If one begins always with the concrete experience of the incarnate Christ, the paradox is solved: the one is revealed as two-fold. The awareness of the double nature, however, is secondary to the experience of the actual oneness of the incarnate Christ, and is only arrived at by deduction from that oneness.[...]
Now, a excerpt on St. Cyril's Christology.
This was the natural result of Cyril's theology of hypostatic union-the human nature did not have its own human hypostasis, and was thus not a separate human entity (the man Jesus), simply the human nature of the divine Word; and the Word hypostansed it.[...]The nature is, therefore, not conceived as an independently acting dynamic (a distinct human person who self-activates) but as the manner of action of an independent and omnipotent power—that of the Logos; and to the Logos alone can be attributed the authorship of, and responsibility for, all its actions. This last principle is the flagship of Cyril's whole argument. There can only be one creative subject, one personal reality, in the incarnate Lord; and that subject is the divine Logos who has made a human nature his own. Equally, however, the incamated Logos cannot be sensibly understood purely in terms of his own 'proper' divine characteristics (as he would be before the incarnation) since he is now the Logos-acting-in-the-flesh, and in accordance with the conditions of the flesh which he willingly assumed, precisely to make use of those capabilities directly. In other words, for Cyril the Logos did not simply assume a body, as Apollinaris imagined, he assumed a human life and all the relativised conditions that are applicable to that. Cyril constantly reminds his readers that in christology one must not speak of the Logos as `Gymnos' (ie. naked, in his divine characteristics) but as `Sesarkomene' (enfleshed). The subject is unchanged, the divine Logos, but that subject now expresses the characteristics of his divinely powerful condition in and through the medium of a passible and fragile condition. Cyril, by preference calls this economy a Kenosis or self emptying, following the terms of Philippians 2.6-11, a central text in the debate.[...]In the first place [St. Cyril] holds fast to the primary proposition that there is only a single subject referent in all the incarnate acts, in all the psychic and intellectual life of the incarnate Lord, and that this personal subject is none other than the eternal Word of God. For him, this primary principle had to be defended against the very suspicion of any compromise, and he did so throughout his life however many paradoxes necessarily had to be invoked to keep it intact. This determined focus explains all his theological motivation.
Excerpt From Byzantine Theology by John Meyendorff:
In Christ, the union of the two natures is hypostatic: they "concur into one person [prosopon] and one hypostasis," according to the Fathers of Chalcedon. The controversies which arose from the Chalcedonian formula led to further definitions of the meaning of the term hypostasis. While Chalcedon had insisted that Christ was indeed one in His personal identity, it did not clearly specify that the term hypostasis, used to designate this identity, also designated the hypostasis of the pre-existing Logos. The anti-Chalcedonian opposition in the East so built its entire argument around this point that Byzantine Christology of the age of Justinian committed itself very strongly to excluding that interpretation of Chalcedon which would have considered the "prosopon, or hypostasis," mentioned in the definition as simply the "prosopon of union" of the old Antiochian School., the new synthetic reality resulting from the union of the two natures. It affirmed, on the contrary, following Cyril of Alexandria, that Christ's unique hypostasis is the pre-existing hypostasis of the Logos; that is, that the term is used in Christology with exactly the same meaning as in the Trinitarian theology of the Cappadocian Fathers: one of the three eternal hypostases of the Trinity "took flesh," while remaining essentially the same in its divinity. The hypostasis of Christ, therefore, pre-existed in its divinity, but it acquired humanity by the Virgin Mary.