@GracieGirl,
Jewish is a race with the warning that the term "race" is a difficult one that has many reasons. Being Jewish involves much more than religion or ancestry. It involves culture and ethnicity.
It sounds like you haven't read the Bible much. That Jesus was Jewish is a key theme in the Christian Bible.
It was very important to the writers of the Gospels (i.e. the first four books of the New Testament) that Jesus was portrayed as following the Jewish religion. They all had Jesus speaking about following the law of Moses (i.e. the founder of the Jewish religion system) several times.
In two of the Gospels, the genealogy is carefully detailed to claim that he was descended from King David (and important ruler of ancient Israel).
Yes, Jewish is a race. In fact, I know people who are Jewish Atheists.
And yes, in the Christian Bible that Jesus was supposed to be Jewish.