It depends entirely on the state you are in; however, I think the answer is likely yes. Because you were seperated from your husband, the presumption that a child born in wedlock is the child of the husband does not apply. Your husband can sign the birth certificate, however, if the other man files for paternity he can likely get a DNA test done based on the fact that you two had a relationship when you were seperated from your husband.
Depending on what kind of a guy this is, he may agree to allow your husband to adopt his child (if the child is his) in exchange for not having to pay child support. You might want to consult a family law attorney licensed in your state on this one.