Her husband deserves to know. It would be morally wrong to keep the information from him (if you think about it, 3 out of the 4 people involved know, and are able to make decisions based upon that, EXCEPT FOR HIM). How fair is that?
He should also be told because his wife is likely LYING to him about it (if she's even told him anything at all), AND, your husband's girlfriend is almost CERTAINLY lying when she says her husband knows all about it. Either that, or your husband is lying to you.
Keeping track of all these lies??
Thirdly, it just plain WORKS. Most people are not willing to risk their marriages and their families (do they have kids?? good jobs???) when push comes to shove, and the exposure often ends the affair very quickly.
Affairs thrive on secrecy. Shine the light of day upon it, and the roaches usually start scurrying.
Based just on what you've told me (I haven't followed your sitch), this sounds like a very deep EA on its way to becoming a PA. I hate to say it, but if it were up to your HUSBAND, it would probably be a PA already -- it sounds like she's resisted him so far (but likes the attention). Eventually, she will break down and give in, and give him at LEAST enough physical "attention" (I'm trying to be polite here) to keep him coming back and giving her more emotional validation.