Do you have a dirty linen basket? Put dirty things in there. There's absolutely no reason for clean and dirty stuff to get mixed up! All adults are responsible for putting away their own clean laundry.
If you dp is complicating matters just don't touch any of his laundry. Don't sort it, wash it or put it away. Be firm.
I do a wash most days and don't use the tumble drier. We have one large airer and one small gate fold airer. The gate fold airer is for small items like underwear and it gets stood up opened out in front of the big radiator in the hall. The large one stands next to a dehumidifier in the kitchen and moved out to the patio or dining room when we are cooking so that the clothes don't smell of food.
Today I am washing sheets and pillowcases and white underwear.
Tomorrow it will be a sports wash of DH and DS sports/gym clothes and coloured socks and pants.
The next day it will be light coloured clothing - joggers and t-shirts and nightwear, shirts - that kind of thing.
Tuesday probably a dark load.
Then coloured towels and cloths.
Then white towels and tea towels.
Plus a load of jeans and trousers for everyone - I'll do that on the dryest, warmest day so that they can go out on the line.
Our clean washing doesn't always get put away straight away, no. But it certainly doesn't get mixed up with dirty stuff. Sod that for a game of soldiers!