So are you talking about the ones that are 'pre-folded' with a stitched down overlap in the center like I used for my oldest two?
The ones with the overlap seemed to be made of fabric similar to hucktoweling and were folded in such a way that there was double thickness at the edges and triple thickness in the middle 1/3. I'm sure you could use flannel as an extra lining in the middle if you wanted to.
We used 'plastic pants' that were sort of like bloomers with elastic at the waist and legs to keep the outer clothes dry/clean. Some of these were 'built-in' to shorts or bloomers to match an outfit. For instance you could do pink with ruffles for a girl or denim with a pocket for a boy.