What are the stipulations on getting joint custody of a child?

My fiance just found out he has a 10 month old. He already pays his child support for two girls and I have my 2 kids. We don't make a lot of money. The mother of the child does not work, she lives at home with her parents who she says is pretty much well off. We live in the same school district of the child. What are the odds of getting joint custody?