This disclosure relates to a composite comprising (a) a rubber layer comprising a cured rubber and optionally a first copolymer having carboxyl groups or anhydride groups; and (b) a foam layer comprising a crosslinked ethylene vinyl acetate and optionally a second copolymer having carboxyl groups or glycidyl methacrylate groups; wherein the foam layer has at least one surface adhering to the rubber layer directly, and provided that either the first copolymer or the second copolymer is present, and the composite is free of glues or adhesive films in the interface between the rubber layer and the foam layer.