I think that this comes under the Communication of the Attributes in the Person of Christ.
Christ had the Divine Nature which included: Person of the eternal Logos, Son of God and Second Person of the Holy Trinity. This Divine Nature came to earth and was born of the Blessed Virgin Mary, the Mother of God. This resulted in the Personal Union - True God and True Man.
Each nature has it own essential characteristics. They are shared in the same Person. The Son of God is human because He was born, lives, grows, get tired, must eat and sleep, suffers, and dies. The Son of God is divine because He is eternal, all-powerful, all-knowing, immortal.
On the cross both God and man died for our sins, Luther said that if only a man died on the cross, he would be a poor savior.