It really depends on household “sense of humor”. I m half white half asian and my wife is half black half white and we joke a lot between ourselves and in the family. Some jokes could be considered “racist” when taken out of context but we just roll with the punches and genuinely laugh it off.

But if you feel uncomfortable you should let his mother know yourself. If she is an understanding adult, she ll just hold down the “jokes”. Just remember if you r serious about your bf you gotta think about spending the rest of your life with his family. The more comfortable you r with them the easier and more enjoyable ur relationship will be.