I have had a few friends volunteer to spend time with him for me to get away, but if I mention it to him, he feels I am getting a babysitter. I cannot get away from him. If I'm not following him around to see what he's into, then he is following me around to see what I'm doing.
Your husband is sick and his dignity is offended. He hates his own situation. That's understandable. This isn't about you.
Ideally, the person taking a shift would be some long-term friend of his, too - a man? That would make it easier to start. But whoever it is, just tell him that he needs someone around and that this friend will be there to help. Doctor's orders.
Good luck. Please let us know how this goes for you. Remember - you deserve this for your sake but also your husbands. You want to be around to take care of him, so you need to take care of yourself.