A.,
The burden of proof is in fact his. After the baby is born file court papers for custody/child support and if he contests paternity he will be forced to take a test and he will be forced to pay for it when it is found out that that child is in fact his.
I know it seems like a hassle and right now I'm sure it seems like much more stress then you could possibly deal with, but as my lawyer constantly told me.. It's not about you, it's about what is best for that baby. And that child deserves to be supported and taken care of. And your ex has a responsibility to do that for that child. And he owes it to you to help you out. You are the mother of his children, that deserves respect and you deserve to be treated with such. And that child deserves to know it's father just as surely as your other children know him.
I hope that everything turns out okay. I've been through it, I know it's hard and I know it's scary but you can do it. If you ever need to talk or just to vent I'm here as well as countless others I'm sure :)
Take care,
Nikki E.