Jesus is not a "natural man" in the sense as the same limitations as us on earth because He now has a new type of body. This is the same form as His old body (i.e. He looks the same) but as I mentioned the "glorified" body is in every way superior to the "natural" one. Our currently bodies decay and will die. All those who believe will receive as body like Jesus.
Jesus confirmed He is indeed a man with a physical body, eating physical food in Luke 24:39-43 etc. Some might say this was illusion but the same type of flasehood exits in the WT with regards to Jesus' resurection body. In similar ways, other heresies exists amongst other groups which claim Jesus death and/or resurrection were were just an illusion. It is clear that the disciples thought Jesus was appearing only in spirit, not physically but He showed them otherwise.
I think these verses speak clearly enought regarding the nature of Jesus.
Hebrews 13:8
English Standard Version Anglicised (ESVUK)
8 Jesus Christ is the same yesterday and today and for ever.
Stephen