Race used by statistics and government is of course a simplification, so if you have to do it, you kinda need to embrace the simplicity of it.
Personally I think the term caucasian works well.
Jewish has of course a historic racial component, but practically (again, the simplicity) is more like an identity such as "hispanic". So if you are white hispanic, you're white. If you are jewish, you are white. If you're a black hispanic, you tick the box for black.
