There have been many good answers so far. I hope my imput will be able to add to the discussion.
We must start in the beginning. We know from John 1:1 that Christ coexisted with the Father and yet was truly God. This was before He took on Flesh. We find in Hebrews 1:3 and Colossians 1:15 that Christ was the true image of the Father, the perfect image. This is where we find that Christ not only possesses a Divine nature before His Incarnation but is, infact, inherently a Divine Person.
It is after this which we come to the creation of human personhood and nature. Man was not solely created in the perfect image of God, which is Christ, but also in likeness. In likeness we find degrees of separation. It is inherently not an exact reflection. A good example is the painting The Treachery of Images by Rene Magritte. It is a painting of a pipe with the words (in French) “This is not a pipe,” written under it. It is a image of a pipe, but not an actual pipe. A perfect image would be an exact replica of the pipe, therefore an pipe in and of itself. The painting is an image and likeness as it is distinct from the actual thing. So too is man. In our likeness, we are “like gods” but not God Himself.
We now see that mankind is separate from the divine nature and personhood. In creation, the human person is a union of body and soul. Man’s nature comes about through the soul’s individuation in the body. It is inherently tied to Man’s action. This is opposed to God’s nature as it is inherently one with his existence. His nature is His existance, thus the Divine nature cannot be separated from divine personhood.
At the incarnation, Christ did not shed his divine soul to become a human person, instead the Divine Person, with His Divine nature, to become man. instead the Divine soul, the perfect image, took on likeness. The divine soul, along with its nature was made flesh and in doing so, took on a human nature in its act of living. Thus, Christ experienced humanity through His human nature. This included temptation. Mankind, in its likeness and imperfect image can choose something which is oriented to something other than God. The soul may choose sin over God, but the opportunity to sin (temptation) is offered through its act within the world, that is, through its nature. This opportunity for sin is inherent in the human nature It results from the enactment of man’s free will to choose something other than God. The inclination to sin results from the Fall of man"s nature.
This is where we find the difference in the temptations of Mary and Jesus. Mary had a human soul and thus could have chosen to orient her act towards something other than God, but did not. Christ, as He had a Divine soul instead of a human one, was offered the opportunity to sin in temptation through His human nature, but could not as the inherent nature within the Divine soul could not deny Himself.
Thus, Christ is a Divine Person with a Divine nature but also took upon Himself a human nature in the Incarnation. From that point onward He had both a Divine and human natures.
i hope this helps.
God Bless,
Br. Ben, CRM
P.S. I am sorry for any grammar or spelling errors.