If there is a confrontation between Mike and Mr. Schmidt (Henry) in the future, I think it would be far more powerful if Abby referred to Henry as Mr. Schmidt and accidentally called Mike "Dad" due to how sleepy she is.
That would speak volumes and be so powerful: I mean, Mike had to be an older brother, father, and mother to Abby starting from when he was 14/15. He raised her, helped her with her homework, soothed her whenever she had a nightmare, cooked warm homemade meals for her, and so much more. Mike was the father Henry wasn't, and I feel he'd take great pride in telling that as he guided Abby back to her room.
Having Abby calling Mike 'dad', if we ever get a confrontation with Mr Schmidt- who would be trying to get back in their lives (I think that's how the confrontation would be like in recent times with Mike being in his 20s and all). And then Abby is somewhat awake by the fightin' and how loud it's getting (or if she was close to it from the start; as in the fight being in the kitchen and all), and then just calls Mike her dad and her actual dad just by 'mister' or his first name (which is Henry <- a Mike Emily truther till the day I die).
It would be SO impactful to both of them, yk. And you said the words from my mind, of Mike being the family that Henry wasn't.
I also see Mike takin slight pride in it, to show that he IS capable of caring for someone, but he'll also be affected by how Abby would say it. I think Abby would say it in a nonchalant tired way and mix it with genuine curiosity (I think she'd just ask "what's going on dad?")