I would suggest that as your husband has mh issues, he might not be best placed to take over this role in its entirety.
WTAF????
He has depression. Are we taking kids off those with depression now?
Shall we pack him off to Bedlam?
What shall we put down on the registration book as the Reason?
Went doolally as his wife was cheating on him...? Or will Cuckold do?
for whatever reason she deemed acceptable she had multiple affairs for periods of time and clearly isn't going to make this dead relationship work, because fundamentally she doesnt want to. Or can't. Matters not.
She was NOT thinking of the kids when her feet were in the air. she was thinking of herself.
she is not thinking of her kids now, she's thinking of herself.
This man has depression, is on multiple meds and as he has not cheated, why on earth should this woman be able to boot him out of his jointly owned home. He can get support to keep his family unit together. In fact actually, once it's out there as to why she is no longer on the scene, there will be more admiration and support for her than there would be for a woman. He will cope, in fact NOT having this awful toxic environment will really help. Within days of the OP leaving I am sure he'll start to feel better.
OP, you cheated, your actions are causing pain, YOU chose to take that course, YOU need to do the decent thing and allow your family to heal from the pain and damage YOU inflicted on it. YOU need to go.