Thank you for your responses. My husband hasn't behaved this way with other people; he really does seem to have lost his mind when it comes to her.
As for the not trusting: they broke one of mine and my husband's major agreements (no oral sex or intercourse until both parties have been tested) while they were drunk. This is a HUGE red flag to me.
There was a situation in which her actions (or lack thereof) affected me, my husband, and my partner; my evening with my partner (and a very emotional and much-needed discussion) was interrupted because she forgot something at home and my husband was insisting that I bring the car home so he could take her to her place. I did, and was very resentful about it, and my partner was extremely uncomfortable with the whole thing. She didn't even apologize for inconveniencing us.
She and my husband had a condom break, and thank god she can't get pregnant (or so she says) but I didn't find out about this until almost a week later. I was livid and felt like he had been lying to me (though he says he didn't want to tell me when I was out of town.)
I don't even know if I'm being unreasonable anymore. I can't think objectively about this at all. I don't think that she is adding anything to my husband's life except stress and drama. I don't know what would have to happen for me to trust him again, but I have been reluctant to be close to him or spend much time with him lately. He has been jealous of my other relationship, and I wonder if he's trying to get back at me in some way (though, for what? For having a happy, stable, loving, honest outside relationship? That seems ridiculous.)