he hasn't had a single word from his line manager since he was suspended.
To be fair, as you acknowledge, they simply can't be in contact while the investigation is in progress.
Now the decision has been made, his LM has to follow a procedure, they will be constrained in any communication they make.
I'm really sorry OP. I feel enormously for you; however, I do think your DH sounds massively immature, and you are doing a lot of looking after him.
I think Bluntness' advice is correct here.
I'm also not convinced he was a great employee bar one isolated misuse of social media; warning bells rang for me throughout & I do agree that they were looking for a reason to let him go, I suspect there's a complicated story there.
I hope this time he can learn from this, move forward & get help if needed.
I hope you'll be ok, most of all.