Yes, but a Christian will not admit that Jesus is a prophet and not the Savior. Islam recognizes Adam on the same order as Jesus of Nazareth. And there is no way Islam is going to demote Mohammed and call him "a" prophet. He is THE PROPHET.
There are Christians throughout the Middle East. It is also interesting to remember that there are Muslims who peacefully live in Jerusalem. I don't think Hezbollah recognizes them much, though.
Muslims believe in the Virgin Birth, and while their story of this is different, that does not prevent some Muslims from honoring Jesus by celebrating his birthday.