I'm hoping that @curious79 is reading and taking it on board, and is going to do something, even if she doesn't comment.
This isn't people being hysterical or over reacting or being overly sensitive, this is your husband hurting your daughter, mentally and emotionally, and you letting it happen and making excuses for an adult while blaming a child for being 'thin skinned', and some of us sadly recognise his and your behaviour from experience.
How would you feel if this were her bio father? Or a teacher? Or one of her peers treating her this way?
It won't be easy to face, admit and then confront. I had my own little battle with it all, although no partner involved, with the way I treated my own DD - the same way I was treated - and I was damaging her and our relationship. I changed it, it bloody scared me when I realised I was doing exactly what my mother did and made my DD feel exactly like I did. The person I should have been protecting the most was the one I was hurting and it's incredibly hard to admit that.
She's 20 now and we have an amazing relationship, but I still have to remind myself sometimes to not respond as my mum did - she constantly looked for a way to blame me in any situation for just about anything, never had my back, the first question was (and to some degree is, although I admit she's made a concerted effort to change) "What did you do to make that person treat you badly?" No matter what the situation was. No one could ever be unfair or horrible to me, because I deserved it somehow, I'd always done something to warrant it. That's not to say I'm soft, and DD has a good sense of personal responsibility but is balanced because she doesn't think everything is her fault.
Even my cousin once, when we were around 5/6 asked his mum "Why doesn't Maverickess' mum like Maverickess?" Out of the mouth of babes and all that.
I've worked through a lot of it, but there's times that it still trips me up - like this thread. So I'm going to hide it now because I've highjacked the thread enough, people don't need to be reading my story - this is about that young lady, and because it's affecting me personally more than I want it to.
Thank you to the other posters for your kind words and my heart goes out to those of you who have experienced the same.