Have a good think about whether your relationship is really what you want before you give up your second job.
I think that even though he doesn't want to work himself, he resents the freedom your two jobs give you, your opportunities to meet people and talk about stuff other than what was on the telly, and the fact that if it ever suited you to leave, financially you would be in a strong position. He is trying to achieve control over you. Don't let him because he will become more and more demanding. And then he will start to complain that you don't have the money to enjoy yourselves, whilst simultaneously making it impossible for you to earn any by insisting that you stay with him.
Just as a matter of interest - does he do anything in the house while you are out? i.e. cleaning, laundry, washing windows, preparing a meal for you when you come home.
Your extra long shifts are a temporary thing soy can enjoy your holiday. Please remember though, that you really need to socialise with people other than your DH - if you give in to his demands you will end up stifle and resentful and very depressed yourself.
You obviously love him - have you tried suggesting that he do something outside the home to give him an interest and stop him getting bored? Even if he can't take the stress of paid work, he could volunteer somewhere - his doctor could protect his benefits y writing a letter stating that he could do "therapeutic" work which would help his mental health condition. It would probably do him the world of good to get out an do something, as anther PP pointed out.
If, as you imply, he no longer has a mental health problem, thence certainly should come off his benefits and get a job. People are telling you to report him, but he's your OH and it's very difficult to do that. It would certainly end your relationship, which you value.
If I were you I would think about what he actually does fro himself and for you before I gave up my 2nd job. It looks like the concessions are all one way - you conceding to him - rather than each of you offering something. "If you resign one of your jobs, I'll get some part-time work/ volunteer at a charity shop/ make sure your dinner's ready every evening etc.
At the moment you are both financially and emotionally independent - don't throw this away lightly. Giving up your job will have a psychological as well as a financial impact upon you. Make sure you really want to do it.