ACK! So sorry you had to see that.
It's sad to say, but I think your WH is lying to someone on FB about his status or where he lives or something to that effect. The only other explanation is that he got hit on the head pretty hard and forgot that he lived with you and his children, and thinks he lives back in his old house (have you checked his head for any bruising or trauma marks?).. Presuming he has no head injuries, I'd go with: he is continuing to screw around on you and is lying.
I had a similar situation, though, at the time, I had no idea my WW was screwing around on me.
We were at Disneyland last year and she was insistent that I do not post pictures on my FB timeline that showed her and me together. It seemed like an odd thing to say (note: I wasn't too big into FB at the time, and thought maybe that was maybe normal that umm.. a wife wouldn't want to be seen with her husband on FB? I don't know WTF I was thinking, but anyway...). Well, I later found out through her disclosure that the reason she didn't want us to be photographed together on FB was that she was FB Friends with her AP and with friends of the AP, and she had told all his friends that I was her "ex-husband" (note: we were not ex's at all, we stayed in the same hotel, were married, and were in false R). So, it would've looked quite weird if they saw her happily with me at Disneyland. Would have kind of spoiled the fantasy of the A, ya know?
So, I can say from experience, if he's doing shady shit like that on FB, it is likely directly related to the A. Sorry you have to hear that or experience it, but that's almost guaranteed to be what's going on.