Ernst suggests: foam sandwich
A google search on foam sandwich netted the following description:....One nice thing about this stuff is that it comes with its own thin fabric backing, so you can sew this directly to the upholstery itself rather than using some kind of muslin backing to keep stitches from pulling through the foam, and you can then glue the foam-and-upholstery sandwich directly to the thin plywood (or whatever) upholstery-bearing panels.
Many hits for foam(core) sandwich, too.
HTH!