Yes--I was still in my separation period when I became pregnant with my daughter by another man.This was in Arizona. My ex-husband didn't create problems for me as it had been a year since we had lived together anyway. He signed the Divorce papers and there was an option that stated I was pregnant but the baby was not his. Then when my daughter was born, I pursued support from her father. There was a court ordered DNA test.
If that is not the case in your state--If you are still married when the baby is born--you will have to file a motion for a DNA test to prove your husband is not the biological father. He will still have to relinquish his rights as well since he is still legally going to be the father. Once that is done, the biological father must either sign an affidavit of parentage or do a DNA test and become court ordered as the father.