If it weren't for your husband, what would the situation be?
How would you deal with it without him?
Because, if it were me, I'd accept that she is an adult who gets to make her own mistakes, but make sure she knew I was there for her, if she needed a shoulder to cry on.
Your husband is trying to shield your DD from life's tough lessons, and at some stage, he needs to let go. She is unlikely to appreciate what he is trying to do for many years, if ever, and by then the damage to their relationship will already have been done.
If you insist on siding with your DH, you will be damaging your own relationship with your DD.
You need an adult relationship with her now. She's not your little girl, anymore.