Your dh is an unrealistic dreamer. She's not going to magically "adjust", someone needs to help her to adjust (not a great choice of word) and that someone is not you! Does he understand that kids need to be taught stuff? That raising them doesn't mean just feeding, clothing and sheltering them? 

I've seen your bio - is sd the only one that's his? 

I have a very similar experience except my husband has been in serious denial. After a giant fight I finally got him to agree to cameras in the house as SD reports everything to BM too (mostly lies and accusations sprinkled in with yeah I had fun).

Since the cameras aren't up and running just yet, I can't share my results on that solution but I do recommend you trying that yourself since your husband isn't in complete denial.

Protect yourself and your biological children (if they are still in the home) first.

I don't think SD will like that it's her word against the camera. My lawyer has also been recommending me to get one for my own protection before the SD even showed up as I have shared custody 50/50 with my own kids.

Hope that advice helps. You aren't alone.

You do not and cannot fix this. It's up to her parents.

Have you had a serious conversation with your DH about this? That's where to start. Don't try little suggestions here or there but lay it out about how you feel, what you see and experience. If he reacts with defense and denies (my DH did and still does sometimes) rather than listen and plan with you, then it's time to think about disengagement. 

It doesn't mean you ignore the teen (not a kid BTW) but you do not extend yourself or your time and money for ungrateful attitude. Your DH would then clean up, help her out...he would be doing the work.

My YSD15 is a good one, but there are major issues that the parents do not handle. I do not. I do not clean the entire house myself (she does hers and her laundry but will not help anywhere else house or yard) and DH does not want to have her do this. So I don't! If he doesn't I bring in my house cleaner and yard people. I don't buy special food for her and I don't cook most of the time she's here. I don't plan activities. Just some examples. 

She's 15, not a little girl.  Time to let go of the rope and let SD hang herself.  Have some phone calls with a friend where you start sharing outrageous things that SD will trip over running back to BM. Stuff that when it comes back will make her look stupid with her evesdropping habits.  
 

As for disengagement, it means that you only participate as much as you feel called to do.  Tired of the drama? Don't play.  Dont give it anymore energy.  Her father needs to take of this so you do not have to.  When he starts throwing money at her, remind him he is setting horrible standards that will make her getting a solid spouse a lifelong challenge.   

Why does your husband not hold her accountable as far as cleaning up and helping out around the house?

Kids don't always "just adjust". They need guidance and parenting. Waiting around for her to adjust is lazy parenting on your husband's part.

I'm sure she will be "adjusting" until she is 18. Sounds like another enabling DH that throws excuses out there.

My DH has listed every excuse in the book for the last 6 years. He is slowly realizing it's HER. DH used to blame the teacher, friends, BM, BMs boyfriend, ME, her ADHD, her being a product of divorce, low self esteem, etc. DH told BM the other week that he thinks SD11 plays both sides, milks the situation, and is manipulative. Finally taking off the rose colored glasses!