Maybe I can make myself a little clearer. Is there a mold and mildew problem with outdoor bedding?

Yes usually the top layer can get some mildew growing and deeper layers if it gets soaked.
There are some great new mildew proof fabrics that would work. I always wanted an old timey glider long enough to lay on for outdoors. I remember my Bobba's(grandmothers) porch having one and using my foot to keep the glider going until ,,yawn ,I fell zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzz
Of coarse the first Flight Safety pilot that swoops his noisy plane down would wake me here!

A fabric called Sun-brella is resistant to mold and mildew. I wouldn't put a regular mattress outside here but there are loungers that would work for nice naps. You need something that dries quickly after rains. No matter how far under cover it is, it will get wet!
I have one (Walmart $160) that I love. It's not Sunbrella but one of these days I plan to recover it and that's what I'll use.

This is the covered portion of my screened patio.

Thanks,solestice! I've heard of Sunbrella on other forums but haven't used it. Sounds like the way to go. I love your patio and especially the brown striped double (whatever you call it)! I'll bet that's a comfy place to snuggle up.

Goldenpond, your Bobba's porch reminds me of going to my Aunt Irene's. She had a porch swing and I spent many an hour laying in it and moving it back and forth with my big toe. :)

A hammock on a stand is also very relaxing in a screen area.

Mammie,I do hope you hear about your offer soon and can realize your Florida dreams.
Kate,very relaxing area you have created and lovely and
inviting. Am I inviting myself to a nap at Kate's?
Just kidding.

Felix

Felix - you are welcome anytime! Bring the puppies and we'll let them run with the shelties. I'll send you home with some plants too!

Thanks, Felix. You have puppies? What kind? I love me some puppies! :)

JoAnn Fabrics sells the Sunbrella fabric. Try an air mattress until you find something better, but for looks, I'd also go with the hammock.