DP isn't my DS's father, so I take main responsibility for him. He still helps out where he can, not out of obligation but just because he wants to. We don't really have a set "I do this and he does that", we just take turns depending on who can be bothered doing it! Lol. But I always make him take out the bins!
If he's done a long shift at work, I usually make him go relax afterwards while I cook dinner/do cleaning. He usually wants to help anyway, but I ban him from the kitchen and order him to sit down!!!