I would say I get it from the Fathers, such as +John of Damascus, who writes:
Confessing, then, the same Jesus Christ, our Lord, to be perfect God and perfect man, we hold that the same has all the attributes of the Father save that of being ingenerate, and all the attributes of the first Adam, save only his sin, these attributes being body and the intelligent and rational soul; and further that He has, corresponding to the two natures, the two sets of natural qualities belonging to the two natures: two natural volitions, one divine and one human, two natural, energies, one divine and one human, two natural free-wills, one divine and one human, and two kinds of wisdom and knowledge, one divine and one human. For being of like essence with God and the Father, He wills and energises freely as God, and being also of like essence with us He likewise wills and energises freely as man." [Exact exposition of the Orthodox Faith, Book Book III, Chapter XIII]
His two natres are united in one Person, but are not mixed. Thus, Christ is one Person, with two distinct wills and two distinct natures, united but not mixed.
This doesn't exactly say the two natures do not mix, Kosta. I don't quite understand what you mean by mixing, but, for example, there is the episode where a woman touches Jesus's garment seeking a cure, and His strength is drained from him. This, in my mind, is mixing in some sense, because His divine nature did not get drained of energy, and His human nature did not effect the healing.