I've been doing my own laundry since I was pre-teen, so has DH. So it was pretty natural for us to just do our own. Also, our clothes normally require different cycles: DH doesn't sort light/dark and does everything on cotton warm. I sort colours, as well as delicates/cotton and cold/warm. So many of my loads are irrelevant to DH"s clothes - and he always has enough for a full load of his.
Either of us will call out to the other, for example, asking if any underwear socks needs to be added, or if I don't have a full load, I'll add some of DH's. DH does DD's school clothes in with his, but I do her other clothes (which are mostly cold delicate washes). I've started training her in her own washing, even though she's only 7 - she's really into her clothes, and I want her to understand if she wears three outfits a day, that makes for more work!
We each have our own laundry baskets - well, DD and I have laundry baskets. DH has a pile (inside of which is a basket, somewhere, I think...) of clothes that he has worn but some of which he intends to wear again. I have now learned to ask before just adding some of his clothes to my load, after one day when I washed all of his trousers and he had to wear an old ripped pair. I did once try to help him by "catching up" his laundry and washing it all, but it didn't take long to return to the giant pile and I have better things to do with my time than figure out what clothes he wants washed and which clothes are just holding for a wear-again.
Either of us will do the sheets/towels - usually me now, as DD thinks changing sheets is great fun and so it is something we do together.
I've never really seen it as a big issue, and if it makes sense for another couple to share, it doesn't bother me! But we're neither of us putting on partial loads or anything like that. And DH does laundry so infrequently it's not like there's much of an issue of scheduling.