Unashamed cat lover here (we have several, all rehomed/adopted at various stages of kittenhood/adulthood when no one else wanted them).
They do sleep on our beds - they all seem to have decided who their own 'designated human' is between them (humans don't get the choose which cat is 'theirs' - it's definitely the other way round!). The youngest one, who we had from kittenhood, is now nearly 4, and thinks I'm his mum (he had a very poor start in life, and latched on to me when we adopted him because I was there all day when others were at work/school). He sleeps on the bed with me every night - not on the pillow (I'm guessing that's his choice!) but he likes to snuggle up on the duvet with a paw draped over my arm so that he knows I'm there. It's unbearably sweet! They also love to be on the sofa with us (it's leather, but I wash the cushion covers weekly, as I do the bedding.)
Dogs, however - no, could never have a dog on the bed, or the sofa. We don't have dogs, and none of us are dog people, but friends have dogs, and there's one huge advantage of cats over dogs: cats don't smell of wet/dirty cat. Ever. Dogs nearly always (unless they're really kept scrupulously clean on an almost daily basis) somehow do. Cats also don't go often out in the rain unless they want to (which is rarely!) whereas dogs need walking no matter what the weather, so wet dog can't really be avoided a lot of the time, and I do understand that.
But the reality is the house, the sofas/chairs and our beds don't smell of cat(s), wet or otherwise, and we have covered indoor litter trays (well-used) as well. In addition, I work from home, and sometimes have clients coming to the house, and they would not be backwards in coming forwards if the house smelt unpleasantly of cat in any way at all! Whereas I know people with just one dog, beautifully cared for, lovely and looked after, but their houses (sorry) smell of dog. It's just 'there'. I believe the difference is in the fur and how the two species deal with water.
So you go right ahead, OP, and sleep with your cat, but the suggestion of having clean bedding for your OH when he stays over sounds like the perfect compromise.
Cats are the best! (Bias completely obvious - apologies to all the dog people out there!) 