The fact that he dropped out of uni after withdrawing to his room indicates fairly major problems. It's quite possible that he is suffering from depression or anxiety or both. To not even manage to sign on implies problems coping with that situation, if it's not just bone idleness.
The fact that he now only goes out once a week with your husband adds to this picture.
You need to get to the bottom of the what the issues are here: is it simply laziness & apathy; or does he need mental health treatment to get him back on track.
I really agree with Kernowgal's post:
Anyway, upshot of this is: make him an appointment at the GP and get him prescribed with ADs or beta blockers or whatever he needs. Then give him a list of jobs around the house, nothing too onerous, but with deadlines. I firmly believe that someone's self-worth is dependent on them feeling like they're making a useful contribution, even if it is just ticking off a load of housework tasks that someone else has asked them to do.
I don't think it is at all sensible to encourage him to travel abroad in his current state, if he has difficulty making friends, he could spend a very, very lonely time that would not be good for his mental health.
Perhaps that could be a longer term goal?
As per the cleaner: you work full time, you pay a cleaner if you want to. Give your husband the choice of either a) cleaning properly or b) paying someone else to do it.