Sliding off into heresy if you're not careful here... Jesus was a human being, in all aspects. "Fully man" and "fully God" at the same time is howthe Creeds state it. Anything else is officially heresy.
But he also (Phil. 2) divested himself of all aspects of divinity in order to be human.
Personally, I suspect that some of his teaching comes from the celibate Essene sect (or is at least based on aspects of it) so I think it's unlikely.
Mainstream Jews, however, would have regarded him as highly unorthodox (to say the least) if he hadn't been married. A rabbi without a spouse, to them, was almost as taboo as a Catholic priest WITH a spouse.
What makes you think that Jesus was a "mainstream Jew?"
Yes, it would have been unusual; but not unknown: John the Baptist was probably celibate, and I'm sure that the apocalyptic sects that existed at the time also had some pretty strange ideas. It's probable that Jesus had more in common with those people than he had with the "mainstream"; certainly if his disparaging remarks about the Temple heirarchy are anything to do by.
But it's not impossible that he was married; in a highly male-oriented society it's entirely possible that nobody thought the name of his wife worth mentioning.