Sounds like you are fed up with your lot and feeling overwhelmed. I think the husband 'not doing much' is a red herring. He works FT you work PT, surely the division of household chores should reflect this? You ask how a functional marriage works? By communicating without blame and accusation, sounds like you are really angry with your dh at the moment but I would hazard a guess that he is a handy focal point for a wider sense of dissatisfaction in life.
You asked about routines...
Our routine (we both work FT, he works 14 hour shifts and I can work flexibly so do a lot of work at home so I can be there for kids)
If I'm taking kids to school and picking up
He gets up and goes to work.
I get up, get myself ready,iron kids clothes, get book bags ready, get kids up, give them breakfast, make sure they get dressed and off to school at an appropriate time.
Leave work early to be at home for them, come home pick up work emails, be there for kids to make drink / snack etc, clean / finish work emails while the kids play, make dinner, clean up after dinner, spend time with kids, put kids to bed, clean up, DH gets home at 9.30. I sit down with him and start work again.
If he is at home:
I get up, get ready, wake kids up and motivate them to get out of bed, make sure they have what they need for school and go to work.
He does everything else the same as me in the morning. After school he is there for them and sits with them till I get home, perhaps makes tea. When i get home we do the evening jobs together.
Typically I clean, he tidies (not to my standard though), we share cooking washing etc, he puts bins out, I clean the bathroom. I do the garden which is why it looks a mess.
Our house is a shit tip because we are busy and knackered all the time (also have 2 boys, 1 with SEN, and a chocolate lab who stinks!), gets me down sometimes but when it does I rant and rave, do a deep clean and feel better, he says all the right things and humours me till i calm down - then he tells me what a great job I've done.