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.
Kosta is undoubtedly referring to the language of the decree of the Council of Chalcedon, which says of the two natures of Christ that they are "without mingling, without change, without division, without separation..."
These words, or slight variants thereof, are used frequently in the hymns of the Orthodox Church, especially in the various dogmatic theotokia sung at Vespers.
For the example you use to show any mixing without running contrary to Chalcedon, you would have to posit that the strength that Jesus felt go out from him was proper to his one hypostasis, which doesn't make sense to me.
I'm not sure in any event that the text implies that Christ felt physically drained. Christ simply says that he felt strength go out from him.
Within an Orthodox theological construct, I don't think it would matter, since I think we would say that the strength that healed the woman was proper to the energies of God. Since humans are able to participate directly in and experience these energies, as St. Gregory Palamas taught, Christ in his human nature would certainly do so.