Don't ask him to do things.
Have conversations about what needs doing and figure out between you what needs doing.
e.g. "how are we going to organise getting this week's shopping in?"
Then discuss who will get it, when they will get it, what items need to be on the list
someone needs to do menu planning, the other person can write the shopping list based on what they've decided.
One person goes to the shops while the other looks after the kids/makes dinner (depending on the time of day).
Coming up to the weekend you might say something like:
"right, what jobs need to be done this weekend?"
What follows can be a conversation based on what both of you think is important to get done and you can also figure out when each of you, and all of you will have some time to relax.
So you might decide - Saturday morning let's do laundry, change all the bedding, general tidy up downstairs, Saturday afternoon I'd like a couple of hours to myself to work on a personal project, Sunday morning whose lie in is it? Sunday afternoon I'll take the kids to the park, do you want to have some time to yourself or should we all go out together?
Don't EVER accept responsibility for all the jobs. Don't rate your times as less important than his. Don't ever talk about him "helping" you.
If work needs to be done and it is his to do and he is ignoring it - TELL him to do it.
Don't ask, don't nag, don't wheedly or cajole. Just tell him he needs to do it.
If he still won't then you will need to think about separating. Make sure he knows that refusing to do his share is unreasonable behaviour and you could divorce him for it.