I have been unemployed for about 7 months now and we do ok because hubby makes good money. So I am basically in his shoes.
I have good days and bad days. Some days I feel so down in the dumps that I don't do a damn thing. I allow myself those days. However, I always make sure that by the time the weekend rolls around the entire house is clean. I cook almost every night. Some weeks I may do a bit of clean up each day, other weeks I will do it all on Friday while hubby is at work.
Perhaps if you addressed this with him in a, "I know it must be tough being home all day instead of being out working. I know this isn't an easy situation for you to deal with." lead in it might help. Maybe the two of you can sit down and make a list of things that need to be done around the house. Ask him if he thinks having a schedule would help. If he likes the idea of a schedule then make one out with him. Maybe you can offer to take the task he hates most??? Hubby knows I hate unloading the dishwasher for example. So he did it before he left for work yesterday. It was super sweet and I appreciate that even though I'm unemployed he still helps out.
For me, I tend to feel guilty if he does too much. He works 40 hours/week. I don't work. IMO it is MY JOB to keep the house clean, cook, and make sure laundry gets done. He shouldn't have to worry about that. When I go back to working we will go back to the 50/50 we were at prior to me losing my job.