Like PPs, I think getting someone in to deep clean is a good idea. Once a mess has got really bad, it seems insurmountable. And having it clean and tidy will help you feel better. It's clearly bothering you, and being bothered won't help your recovery.
Once it's clean and tidy, a little bit of cleaning as you both go along will keep it that way. For example, wiping the bathroom basin with a cloth after each use takes next to no effort (I favour microfibre cloths, as you don't need to use any cleaning fluid), toothpaste etc wipes straight off a wet basin. Shower spray after each use will keep the shower clean, the same microfibre cloth can be used for the ring round the bath. Wrap a towel round you, and you'll be dry by the time you've done it. Lav cleaner down the pan last thing at night will render your bog clean next time it's flushed.
But you BOTH have to do this or it's futile. Suggest it to your DH, he has to buy into it too.
Do you have space for a diswasher? I wouldn't be without mine. It's like a cupboard for dirty dishes, so they don't get you down simply be being all over the worktops. Once a day or two, drop a tablet in, press a button, an hour or two later, clean dishes and no cluttered work surfaces.
If you have clear work surfaces, they're easy to keep that way. I tend to wipe a section while I'm waiting for the kettle to boil or the tea to brew. By the time I've had 3 or 4 cups of tea, they're all done. The next day, I do the same with the cupboard doors. Your DH could do this while he makes the tea he brings you. 
A weekly cleaner to do the floors, the stove, dust and maybe change the bedding and that only really leaves the laundry, the online shop and the cooking. I'd go down the one cooks, the other clears route.
Because things have reached a poor state, it makes the whole problem seem massive even for people with good MH, so it's bound to seem insurmountable to you. Getting things into a good state and then breaking things down into tiny tasks will be easier.
I'm a lazy fucker and capable of being a complete slattern, and I know all too well how easy it is for something to seem so grim that you don't know where to start. Doing a little bit regularly makes it much easier. I've suffered from pretty severe depression a couple of times too, so I empathise.