Judith,
That's without question a difficult situation to be in and to deal with ...
That was very inconsiderate of the husband to not be more careful in his dealings outside his marriage.
With that said, the child had nothing to do with it and should have his/her father in its life.
If you're the one dealing with this situation, you have a serious decision to make.
I agree with Lavie that there needs to be some conversation between everyone concerned.
Make sure you remember you're the only one in this situation without fault.
Of course the trust factor has been damaged, but if you and your husband want to make it work, it can. It'll be very difficult, but infidelity does not always have to end up in divorce.
Now, you have to really do some soul searching to see where you're at and where you want to be in this relationship.
If it really hasn't done anything for you then let it go and find happiness elsewhere, but if it's worth it, make it work.
Make him recognize and accept (suffer) his indiscretion, but most of all be true to yourself.
It's all about you right now ...
By the way ...
If you find yourself having to put your private eye hat on like Lavie said ...
Just leave and move on ...
You're too good for that.