My guess is, this woman's husband has guessed the baby isn't his and has ended the marriage. She knows if her husband requests a paternity test, it will come back as her husband not being the baby's biological Dad, so he won't have a legal obligation to pay child support. However, if she requests a paternity test from your husband, whilst knowing full well he's the biological Dad, he will have to pay child support!
Of course none of the above may be correct and your husband is innocent of any wrongdoing. You do have to ask why a woman, who your husband does know and has worked with, would pick him to request a paternity test from, if it wasn't true?! Surely if she knew there's zero chance of your husband being her child's Dad, she wouldn't go to all this bother?!
I do see others point of view though...I could see someone who is innocent saying, 'No I'm not engaging in this, I've done nothing wrong, why should I have to prove I've done nothing wrong'! Equally as several posters have pointed out, if he's innocent and hasn't done anything wrong, why not take the paternity test, because it will give concrete proof.
Unfortunately, your husband's reaction doesn't prove if he's genuinely hiding something or not.