You are not the one who is mental.

It is totally inappropriate, and anyone should be able to see this.  In an initial or intact family, no mom would tolerate her husband and daughter doing this, but for some reason, in step-world some try to argue that they are entitled to their "special" relationship.  Chalk one up for yet another mini-wife.  You can google that term and I'm sure find all sorts of eye-opening examples.  He is treating her like she is his whittle wifey, and you are his mistress.

Unfortunately, because dad and daughter are both getting something out of it (can anyone say "Freud"!), it is a very hard habit to get a DH or SO to break.  You'll have to research the term mini-wife and see what your options are.  Unfortunately, usually this is one of those cases where you have to either turn a blind eye, or get out while you can.

No, you are not mental, and Yes, this is inappropriate.  Don't let anyone gaslight you into thinking otherwise.

I'm going to give you the benefit of all the money we spent on therapists.

No, it's not normal, and our situation didn't sound as bad as yours. There were times when I sat on the floor with the dog while they cozied up on the couch. It felt like a weird threesome to be up there with them. There were times when she hung on him, her giant boobs hanging out. He'd say it was a remnant of her mother's Arab culture -- very touchy feely people.

Our counselor said in no uncertain terms that it must stop. She told my husband to consciously choose a chair so SD had no way to cuddle with him. She told him the incident when SD slept in our bed (alone) because she was sick and that bedroom was closer to the bathroom was wrong -- she should never, ever sleep in her father's bed, even alone. It's just mixing messages in an already triangulated marriage.

Largely, it stopped, but mostly, probably, because SD moved in with a boyfriend and she stopped visiting as often. I remember one time at a family gathering when my husband walked away and SD said to the rest of us, "He's so cute!" and her cousin, who is no fan of mine, said, "Ewww, he's your father!"

There are women who must use sexuality to be close to people, even their father. This stupid "daddy's girl" culture makes it OK. Find a good therapist (it's a crap shoot) and maybe your SO will see it's not good for SD and help her grow up. I don't know why anyone thinks it's normal or OK for a SD to be jealous of a SM. They are different roles that should not cross. Nothing good can come from fostering that dynamic.

My ex's sister and her father had a relationship like that. It was horrible to watch - went on into her 20s and 30s. I don't go around that crazy family anymore but it was so obviously awful the way she would lean over him and fawn over him and generally treat him like a boyfriend - in front of her own mother!! Of course dad didn't see anything wrong with it! If you'd asked either one of them they'd have said it wasn't sexual, but boy was it inappropriate. 

Part of the reason this happened was that the mother was frankly awful - harsh, critical, cold, unaffectionate. I'd bet money it was a sexless marriage. Dad had a number of affairs. He was using daughter as a way to get basic touch in every day life - everyone needs to be touched (I don't mean this sexually). Daughter was doing it because dad allowed it and because mom was unloving. Dad catered to daughter's every whim and basically expected the rest of us to do so as well. She would tantrum and wail. She's still a difficult woman. 

This daughter is messed up. She is 45. Never married. No kids. A series of weird relationships. Eating disorders. Over-attached to the parents. She's not doing so bad now but at one point my ex and I talked about taking steps to get her psychiatric help against her will - but it never quite got bad enough to have her sectioned and she is better now as far as I know - at least she was the last time I saw her. I'm so glad to be out of that family - although of course I'm not really as I have a kid with my ex. 

ETA: I don't have a problem with parental cuddles at all. I cuddle with my son. I'm not worried about cuddles in bed and that sort of thing - my son is 11. My SS12 cuddles with me.  I couldn't g.a.f. about a kid sleeping in the parent's bed if they weren't there. Doesn't bother me. My partner sits right close to his mother on the sofa when she visits and I think that's fine. But sometimes when you see something isnt right you just know it's not right. 

My 2 cents:

Sd is old enough to know better. Dh is old enough to know better. The level of inappropriateness........

If any female in my household behaved that way to my husband i would be suspicious in the least. What possible reason could there be for a woman of childbearing age to talk about her periods with my husband?( unless shes pregnant) I know when I was her age I was very careful to not tell anyone and keep that info private. 

Awhile back i briefly dated a single dad who had a 13yo stepdaughter that he basically raised. He was not a good father or guy in general. However one day he came over and he was furious. Apparently he had punched his BMs new husband in the face for sitting cuddled up on the couch with his hand on the SDs thigh. He told that guy that if he ever even looks at SD inappropriately he'd kill him. He even knew the difference and thought the issue worth going to jail over.(i did say BRIEFLY dated lol). And that was just hand on thigh not face on crotch.

Nope you are not crazy. 

Sorry if I made you paranoid. 

Take a picture of her face in his crotch and post it on social media.