Triple-layered, the answer has to be varied slightly (5-3)
I believe the answer is:
three-ply
'triple-layered' is the definition.
(three-ply means with three layers or plies)
I can't explain the rest of the clue.
(Other definitions for three-ply that I've seen before include "Measure of thickness (of wood or wool)" , "Type of wood or wool" , "Having a triple layer" .)