How do you deal with caring for a husband or spouse?

I agree with funkygrandma Please share all your concerns and any questions you have with the Social Worker, the doctor, the nurses.
The question I have is how were you handling things before he want into rehab? If you were doing well and had no problems it will be a bit more difficult now.
If you were at your wits end, barely holding on and were burnt out before it is not going to be any easier. If this is the case you need to say something NOW.
Is your home accessible? Is it safe for him to get around? Can he easily get into a shower? If he needs help is there enough room for the 2 of you and any equipment in the bathroom?
I guess the big question is
Is it safe for you to care for him at home?
The caring for a spouse is a bit different but the dynamics of your relationship change. Yes this is the person you married and have been intimate with but the intimacies change when you are changing a soiled brief, wiping their butt after toileting, inserting a suppository. Yes he is still your husband but it is now different.

Have you shared your concerns with the nursing facility he's at now? If not, please do ASAP, as they need to know that you're feeling ill equipped to care for him at home, and if need be they need to help you find placement for him.
In your profile it says that your husband has Alzheimer's/dementia. Is he far advanced in that, where you feel he won't be safe in your home, or is he just in the beginning stages? Depending on how you answer that will give you a better clue as to where exactly he needs to be. You know yourself best and how much you can handle, so when making your decision make sure that you're doing not only what is best for your husband but also yourself.
It may be for now that you need to just hire some part-time help to come in to give you a break every now and again, or he may require more full-time help. I guess only time will tell.

I cared for my husband in our home for 24 1/2 years of our 26 year marriage after he had a massive stroke at the age of 48. It of course was easier for me in the beginning to care for him, but as he aged and developed more and more health issues, it became very hard. We went through a lot together.
When he was diagnosed with vascular dementia in July 2018, and later that year almost died from aspiration pneumonia, he eventually came home completely bedridden and under hospice care. I had the option at that time to place him in a facility, but he really wanted to come home, and being that I knew that the life expectancy of vascular dementia is only 5 years, I wanted him to be home as long as possible. I had to hire an aide to come every morning to put him on the bedside commode, but otherwise I did all of his care(hospice only does about 1% of patient care). He lived another 22 months bedridden in our living room.
It's amazing how much we can do for those we love when push comes to shove. But I also learned early on how very important self care was, and that I deserved to take care of myself just as good as I was taking care of him. And that was huge! Without doing that I would never had made it through my journey with my husband. And now that he's no longer here, I am still taking good care of myself.
I wish you the very best as you navigate this next chapter in your life. God bless you.

Becky, have you talked to the NH about having him admitted there as a long term care patient?

Have you asked them about arranging some home care for him?