What was your response to the sit & relax, and the undone dishes?
In our household, we both work full time. We both pitch in to household and childcare. Frankly though, it would get my goat to see my husband browsing the paper while I was dusting the tops of the door jambs. A few things changed to improve our situation.
1. I came to understand that we have different measures for what is dirty and what requires cleaning. He is not being obtuse, he just doesn't see it as dirty, and I am not being overzealous, I do see it as dirty.
2. I had to back off, he had to step up.
3. If I asked him to take on responsibilities beyond those which he usually shoulders (as it is he does the laundry, ironing, much of the cooking, cleans the kitchen, handles the trash, recycling, home repair, bill payment, and does morning school runs and takes our kid to Tae Kwon Do). I need to ask his availability, advise when I need to see it completed by, and then step away and let him do it when and how he pleases. (He doesn't like being micromanaged, I don't like to hover, it isn't a good thing).
4. travel for work or pleasure, makes the other appreciate those tasks which we each do, that fall under the radar, because they are just always taken care of. i.e. I had to disassemble the lemon squeezer thing to clean it recently, and I came to realize that I had never done it because hubs was always the one to clean it. Another example, while in LA, I got a call from the daycare saying our DS had a rash. It didn't even cross my Hubs mind to bathe the kid, because it was something I always took care of.
My point being-
sounds like he isn't wholly a bad egg. he did encourage you to sit & relax.
he is not a mind reader. you might have to ask for help, or re-define your division of labor.
he might take initiative, if he saw the need to do so.
get out of dodge when invited to sit and relax, and set your expectations so that they might be met.
Good luck to you and yours,
F. B.
PS-
for an altogether different strategy, instead of saying you need help, try a you require downtime too approach. If he gets a few hours with his games. Maybe you get a few out of the house. Talk about what would need to happen to facilitate that.