Children only partially fluent in a second language?

I'm not fluent in my second language (Hungarian, third hardest for english speakers), but I grew up with it and there are at least some parts of Hungarian that will always be a part of my imediate family's vocabulary. I'm taking steps to keep as much as I can of my language skills since I moved back to the US, but I really want to teach my children at least some Hungarian as infants. I was wondering if anyone else specifically had children who were partially bi-lingual and how they believe that has benefited them dispite not being fluent.