As far as I know that if your baby is born here, he or she will get the US citizenship automatically but not the mom. However, baby can apply for the parent when he or she reaches 18 years old. In additional, there is a 10 years penalty for over staying in US when the visa expires.......You should consult with a lawyer into this area.
As far as I know, a working permit can not help your husband get a residential visa? Never heard people can get visa in this situation, I will actually doubt if the lawyer tells you do it this way.
Overall, you may need to ask a lawyer before doing this. If you are in NY, you can write to some newspapers such as Singtao, they have a lawyer section for people ask question like that, it is published every Sunday. I will suggest that because US is now quite strict in immigration after 911, you should find out more before you take any risky action. Good luck.