It depends on your point of view, naomi. At the time, Jews believed in the coming of a messiah. Jesus claimed to be that messiah. Some Jews accepted this, some didn't; but all of them were still adhering to Jewish teaching.
And yet, looking back from 2010, we can say that the former group were Christians, the latter Jews - according to the way those religions are defined now. At what point does a 'Jew' who believes the messiah has arrived become a 'Christian'? I don't know. If you have decided for yourself, please tell me?
I also don't know how far Jesus regarded hmself as a Jew. He may have observed the faith's teachings, but his own were different. In particular, Judaism insisted on one god; Jesus's claim to be not just the messiah but both the son of God and God himself seems completely incompatible with the Hebrew god.
(By 'Jewish' in all this, I'm talking about his religion, not his race.)
You needn't presume I am a Christian; I haven't said so and it is relevant to nobody but me.