What's a Jewish Muslim Anyway?

In a couple of my posts, I've referred to my Jewish-Muslim neighbour. Some people found this description a bit strange. What I mean by this is that he is ethnically Jewish (i.e. from Bani Isra'il) but religiously a Muslim. In Judaism 101, they define a Jew as, "any person whose mother was a Jew or any person who has gone through the formal process of conversion to Judaism." Given that he has a Jewish mother (which reminds me -- I have to ask him if the jokes have any truth to them), I figured he's ethnically Jewish.