The traditional Christian understanding of the two natures of Jesus is spelled out in the Definition of Chalcedon:
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Following, then, the holy Fathers, we all unanimously teach that our Lord Jesus Christ is to us
One and the same Son, the Self-same Perfect in Godhead, the Self-same Perfect in Manhood; truly God and truly Man; the Self-same of a rational soul and body; co-essential with the Father according to the Godhead, the Self-same co-essential with us according to the Manhood; like us in all things, sin apart; before the ages begotten of the Father as to the Godhead, but in the last days, the Self-same, for us and for our salvation (born) of Mary the Virgin Theotokos as to the Manhood; One and the Same Christ, Son, Lord, Only-begotten; acknowledged in Two Natures unconfusedly, unchangeably, indivisibly, inseparably; the difference of the Natures being in no way removed because of the Union, but rather the properties of each Nature being preserved, and (both) concurring into One Person and One Hypostasis; not as though He were parted or divided into Two Persons, but One and the Self-same Son and Only-begotten God, Word, Lord, Jesus Christ; even as from the beginning the prophets have taught concerning Him, and as the Lord Jesus Christ Himself hath taught us, and as the Symbol of the Fathers hath handed down to us."
This definition came about as a result of two 5th century theological controversies. The first being the Nestorian Controversy, named after Nestorius of Constantinople. Nestorius argued that Mary should not be called Theotokos (God-bearer) but only Christotokos (Christ-bearer).
Additionally, from
Wikipedia:
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Theodore of Mopsuestia maintained a vision of Christ that saw a prosopic union of the divine and human. This was a union where Jesus was only a man indissolubly united to God through the permanent indwelling of the Logos. (Grillmeir, 428-39) He believed the incarnation of Jesus represents an indwelling of the spirit of God that is separate from the indwelling that was experienced by the Old Testament prophets or New Testament apostles. Jesus was viewed as a human being who shared the divine sonship of the Logos; the Logos united himself to Jesus from the moment of Jesus' conception. After the resurrection, the human Jesus and the Logos reveal that they have always been one prosopon. This oneness of Jesus and the Logos is thus the prosopic union."
Critics of Nestorius (a student of Theodore of Mopsuestia) argued that the Nestorian position separated radically and sharply the divinity and humanity of Jesus. By saying that Mary is not Theotokos, but only Christotokos, Jesus' divinity and humanity are sharply divided. The Divine Logos and the Human Jesus cohabiting the same "space" in a union; rather than a full and real union.
It was sharply condemned by theologians such as Cyril of Alexandria.
But conversely the second controversy surrounded a devote proponent of Cyril of Alexandria, Eutychus. According to Eutychus the divinity and humanity of Jesus were so wholly and completely united as to produce in Jesus a single (mono) nature (physis) of the Incarnate Word. As such this "monophysitism" was, at the Council of Chalcedon, declared heretical.
Chalcedon and its Definition both rejects the harsh division of the two natures of which Nestorius was accused of maintaining, as well as rejecting the confusion or mixing of the two natures into one as Eutychus maintained.
But rather insists that the human and divine natures are neither separate nor confused, but are united entirely without confusion in the single Hypostasis--the one "Personal Reality"--of Jesus Christ. Mary is rightly called Theotokos because her Child is true God just as much as He is true human.
So Jesus is not the in-habitation of the Divine within the human Person; but Jesus is both the Eternal Son or Logos and the true biological offspring of Mary. God and Man, fully both, the natures in-separate and unconfused. Jesus, therefore, is Theanthropos, the God-Man.
-CryptoLutheran