Are Jewish people a race or religion?

My friends and I were having a debate at lunch one day. One said that Jewish can be considered a race because they've been discriminated against (the Holocaust) and they have stereotypes. All religions have stereotypes. She also said that once you're apart of the Jewish faith, whether you're born into Judaism or converted, you're considered a Jew for life even if you start considering yourself as part of another religion and because of that, "Jewish" should be a race. I say that Jewish is a religion because the word Jewish derives from Judaism, a religion. The other girls, one of the them being Jewish, in my group of friends agree that it's a religion and not a race.