I think OP probably knows this all too well, but: don’t throw out your H’s old pillow until he fully accepts a new one.
Ikea has a down pillow
Don’t mess with his pillow! My old one [not gonna say how many years] has been to the cleaners and is kept inside a nice zipped-shut pillow case that can then be covered by whatever fancy one my wife desires. It is malleable into any shape I find comfortable. You can’t buy comfort. My wife tosses & turns and wakes up frequently in the middle of the night. I sleep just fine. Don’t mess with a man’s pillow! 
I’m that husband! Wife has bought me a dozen pillow in last two years. She’s quit trying.
I want a pillow that - when I sleep on my back my head sinks in and the sides go over my ears - BUT I don’t want to sink all the way down to the mattress.
Can anyone help me?
I stayed at a Hilton hotel a few years ago and the pillows there were glorious! I found out that you can purchase them and ended up buying 4. They are down-filled (at least the ones I purchased) and big and you can buy firm or soft.
I was mattress shopping and stopped at a store called the “Original Mattress Factory”. It’s popular in our area. They sell a latex pillow. It probably isn’t what the OP is looking for but it was one my wife and I defined immediately as a comfortable pillow. It was supportive yet soft, rebounded to it’s original shape quickly and didn’t deform. They had other pillow available but not were as nice as the latex. They aren’t cheap at around $60 a pillow but I suspect there will be one in my future. The only this that was a bit off putting was that it smelled vaguely of tennis ball. They indicated that goes away.
Am I the only one who thought the OP was looking for the perfect pillow to “quiet” that finicky husband of hers? 
I’m a latex pillow fan, too. I got mine at JCPenney a few years ago. It’s perfect for me as a side sleeper. They’re not cheap but they’re great quality.
http://www.jcpenney.com/jcpenney-home-latex-foam-pillow-with-cover/prod.jump?ppId=pp5004950902
Thanks for the suggestions. Someone asked why my husband doesn’t shop for his own pillow. The answer is because he doesn’t mind sleeping on the old yellowed pillow. I’ve washed it a couple of times but it’s really old and I’m afraid it will disintegrate in the wash if I wash it again. Costco no longer carries down pillows in it’s stores - they’re only available on-line. I’m thinking of getting two - one soft and one medium. @MamaBear16, I looked at the Company store last night. I think I got some bedding from them years ago and really liked their quality. @patsmom - we have an assortment of non-down pillows here. I can’t justify trying another one. The cost of down pillows really varies widely!
I would let him keep his old pillow until it falls apart.
Take the old pillow to a cleaner that knows what to do with down. Do not wash it yourself. Put the clean pillow in a fresh zippered case of its own to keep any down from escaping. Put the whole shebang in a sham/case of your choice.
Cuddledown will recondition/rebuild their down pillows or duvets. For a price that may not be worth it, but I thought that was interesting.
I travel everywhere with my latex pillow - I love it. I’ve had it for years! It’s also relatively flat. My newer latex pillows are also great, but a little larger - something like this…
I have the down Pacific pillows from Costco and absolutely love them. They are soft and squishy, while at the same time providing just enough support. And lol, my husband has also been sleeping on the same old flat, yellow pillow for years now (his choice). I can only imagine the tiny creatures that live in that pillow - ick!
I wash our down pillows every so often, and when I get grossed out by DH’s disgusting yellow ones (he breathes into them --shudder), I just replace them. I’ve had great luck with the ones from Macy’s.
I haven’t read other posts, but I am like your husband, and my pillow came from the Company Store. It’s there cheapest soft pillow, for stomach sleepers.
ETA Costco pillow was too hard/big for me. Second best pillow came from the sleep number store. It was more expensive and doesn’t work as well.
While Ive heard great things aboutt these http://www.duxiana.com/accessories/duxiana-down. I agree- if he loves his pillow-- well, if it ain’t broke, don’t fix it.
^ yes seems many do not realize pillows can be washed and dried.