I am currently going through a divorce- my husband has had an affair, so slightly different however he refuses to move out. So we are currently cohabiting! I have applied for the divorce and we will continue to live together whilst the divorce is processed- and this isn’t effecting the process as far as I am aware!
I can’t afford to move out and pay both our mortgage and somewhere else and can completely understand your situation.
Seek solicitors advice (use the 30 mins free you’re entitled to- I asked loads of questions this way)
I don’t know if this helps