Call her husband.

I have a situation that is different than your in a few ways but I had the same question about whether to contact the OW's H. I ended up emailing him because I knew that he had info I did not (or so I thought). It turned out that midway through our conversation, he found out info that his wife did not tell him and he freaked! He blocked my email address from future contact and immediately halted contact. I was a bit taken back (because I thought he knew everything). Afterwards, I felt kind of bad because I told him more than he wanted to know. I did not mean to hurt him but ended up doing so. Then... it officially backfired! The OW (who had not been in our lives for over 5 years) now had access to my H. She emailed my H and told him about how her H and I were secretly emailing one another back and forth, talking about them. Since my H knew all about it (he even read the emails between us before she contacted him), he took care of the situation and told her not to contact him again. Long story short... I would have done it again in a heartbeat (because lies and secrets are never good- and I wanted to be sure my H wasn't lying about any details- or potential babies) but that does not mean that I don't have guilt about the feelings that got hurt in the process. Only you can make the right decision because you are the only one who has to look in the mirror at you afterwards. No one else can tell you the right decision (Lord knows many have tried to tell me).

I would talk to the husband in a civil and non-threatening way. Hopefully he would agree there has been enough drama and act 1 needs to come to a close.

The other issue is the relationship between your H and his W. The sooner the truth is known then I see two paths.
1) It is not his child and you have nothing to do with this couple again.
2) It is his child and your husband is involved in the upbringing. All parties have to reach some sort of cordial agreement in the interests of the child.

tell her husband

I would want to know the truth. Call.

I would be talking to her husband!!!!

call the husband