I think a lot of posters have been really unfair here, OP, and I think if you'd started off on a slightly different note you'd have gotten different replies.
From what you've said, it sounds like your DC is a toddler? So you work 20 hours a week, look after a toddler full time around those hours, do all housework, gardening, DIY, and other things. I actually think on balance that you do at least as much as your DP, if not far more!
That said, I do wonder if you could change the routine somewhat? If you were to cook/clean up a couple of days a week, and he did some housework at the weekend would that help? (If he would want that).
I do sympathise with him re the feeling of the daily grind. It's not about family life as such, but with work it can feel like doing the same thing day in day out. I work (technically) 37.5 hours a week, but overrun often. By the time I finish, commute home, do the few chores I have, and have eaten, it's late and I'm knackered, drained and CBA to do anything other than veg in front of the TV. It doesn't really "feel" like downtime, IYSWIM? If I'd had a particularly shit day at work, the anticipation of commuting home and then doing chores is just overwhelmingly depressing! (But such is life, of course!)
I'd imagine though that by the time DH has cooked, eaten and washed up, it's getting dark and DC is probably asleep? Meaning that some of the forms of mental respite eg sitting in the garden, going for a walk, or spending some time with DC, are no longer available to him?
I'm not advocating letting him off the hook - if he gives up cooking or washing up, then he needs to take on some more of the housework, and he'll need to take over with DC. But perhaps arranging routines so that he can spend some time with DC in the evenings - playtime, bed and bath, perhaps - might help?
(Although sometimes we do just need to be able to let off some steam!)