I've been looking at sofa sleepers for several months now. Will probably buy the American Upholstery (same sofabed as American Leather, only in fabric). However, I found a sofabed that has a similar frame as the ones in the photo from minnie. Check out the selectcomfort sofabed link below. The sofa frame is made by Berkline, but the mattress is the type that is inflatable. You plug it in to run the air pump. It inflates in about 4 minutes to 100. Then you can back it down to whatever your "sleep number" is. Mine was about 75. There is a nice foam padding around the blow up chamber and on top of the mattress. It was VERY comfortable and did not feed like a blow-up type bed. They are on sale until the end of June for $1879 for a queen size. The queen size is a standard queen size (60x80). Many sofa beds are shorter. The mattress has straps that snap it to secure it to the bottom of the frame. The frame has a grid look like the photo, but I don't think it had the strapping at the foot end of the bed.
DH is concerned about the increased risk of something going wrong with this type of mattress (leakage, pump, etc). I looked on the Berkline website and they do not make sofasleepers for their own line of furniture. Only the sofa frame for the select sleep mattress company. The frame comes apart so it can be moved easily. The back comes apart from the sides and the bed frame can be unscrewed from the sides for easy moving or when moving to a space that requires a sharp turn.
http://www.selectcomfort.com/sofa_beds/sofa_beds.cfm