[on phone so excuse misspellings]
As corsiKa pointed out, there are a lot of feelings and complexities and personalities in play here. It is hard to answer your question without more information. Some very general thoughts:
He's kind of the enforcer, and I guess you could say I'm the good cop.
1) He may be tired of always being the "bad guy".
2) He may have wanted you to step up for a while, and is finally boiling over.
my husband and her got into it when we got home, and he grounded her for 1 week
Where were you while this was going on? I'm guessing your position is encapsulated in this statement right here:
she's never broken the rules before and is usually very responsible.
Your position seems to be one of secret defense of your daughter. You agree that she should not run her smart-mouth off ("I told my daughter I need her to quit running her mouth and it's got to stop.") but in the secret places of your heart, you think your husband is overreacting on the no-friends-over thing. (I.e.: Yes, she did a bad thing, but she's mostly pretty good, so no biggie, right?")
Now he's not talking talk to me, and my daughter doesn't understand what's wrong or why she's grounded.
Of course she doesn't. She's a teenager, and they always believe that they are the wounded party in every situation, always. And if I'm right about the above, she detects a soft stop in you, and is working that distance between you and your husband to her advantage, reinforcing herself as the wounded party.
Here's my best guess, given the information at hand. Your husband probably feels like he is alone in hostile territory. He has a teenager rolling her eyes and complaining about how unfair he is (and depending on her maturity level, stomping her feet, and bitching on social media about how mean he is, and possibly saying hurtful things like, "you're not my dad!"). Teenagers are stressful and emotionally exhausting and have zero self-awareness at how hurtful their actions can be. And, he may additionally feel some angst and self-doubt because she is not his biological child.
On top of that, his wife does not have his back. Oh, sure, you are trying to remain neutral, but to quote a Latin truism: "Qui tacet consentire videtur," or in English, "Silence implies consent." Your possible silence on the matter of her inviting friends over implies your consent to her behavior.
His ultimatum is extreme, but he probably feels overwhelmed and alone in enemy territory. It sounds like communication is not his strong suit.
Again, without more details, it is difficult to make recommendations. There is some communication that needs to happen between you and your husband. Your husband's initial punishment is firm but not extreme. He's possibly afraid of worst-case scenarios like that she is going to invite boys over when you guys are gone and have sex (and get pregnant, move into a trailer, and go on welfare, etc) or whatever. He's possibly trying to nip things in the bud. Especially if he was wild when he was a teenager / snuck into girls houses when their parents were gone.
One technique to try to understand his position is to do some "perception checking". There are lots of resources on the web on how to do perception checking. But basically describe the behavior you don't understand in a neutral, non-judge mental manner, and then ask questions. Don't defend or justify yourself; try to get to the bottom of his thoughts and feelings before you respond (with love).
Additionally, if your husband is so frustrated with the situation that he feels he needs to leave, then this has probably been festering for some time. Consider marriage counseling. If that is impossible, then consider getting some books about marriage self-help (eg men are from Mars, women from Venus, etc). In the meantime, try to make him feel your support him as much as you can.