You are lovely to post here.
Recognise that depression is a very phsycial illness. Peole relaly can;t get out of bed sometimes, It's like yoru body is made of lead, and the messages the brain is supposed to send to the body to say: sit up, put your feet on the floor, stand up etc just aren't firing.
But, having said that, I'd encourage him to take care of himself physically. Very gently tell him he doesn't have to want to have a bath/get some fresh air/put on clean clothes but he does need to do it anyway because it will help him recover.
Make sure he has a really good diet. Plenty of fresh foods - lots of veg, fruit and nuts.
Get him exercising if he's up for it. Fresh air and nature are good.
If he resists, tell him he doesn't need to feel better during or after the walk - it' snot pressure to get well quickly, but it is a really important part of the process.
Help him access outside help: online CBT, PTSD counselling etc.
Finally - and i mean this seriously - really take brilliant care of yourself. You need a life. See friends, go for walks, watch comedies, make plans, have a weekend break or a holiday, with or without him. If he thinks you're ignoring him or moving on from him, just gently explain you;re not, but this is how normal, healthy life works and you need to live that way so you don't get caught in the spiral. It is very easy for carers of the depressed to get depressed too. It's very draining.