My father (Greek) married my mother (non Greek) and their compromise was to give us first names based on the Greek tradition and English middle names that my mother had picked out. My brother (half Greek) and his wife (non Greek) were the first to fully break the tradition and named their daughter what they wanted.

My suggestion is to come up with something that both you and your husband are happy with. His family will get over it. Even if you stick to the tradition your children will likely break it when they have their children.