Welcome to our forum.
It sounds like there may be some communication gaps here, both in the honesty area, and in the completeness area. We know now (by experience) that "consenting" to something we secretly hope won't really happen is a problem. On the same token, your husband has no business lying about his feelings toward his girlfriend, and she has no business running off having unsafe sex. And how does her man feel about all of this? The four of you need to start sitting down and talking as a group about what's going on, even though it probably won't be easy. You have to be candid, thorough, and willing to listen.
I can't promise that nothing will be a dealbreaker. But really communicating is better than a world where you're just trying to go along with something you feel you object to on a very deep and visceral level. It sounds to me like you aren't happy at all with the situation. So something needs to change.
I hope your time spent on Polyamory.com will help you.
Love means never having to say, "Put down that meat cleaver!"