Composite structures are described that include (a) a first polymer structure (e.g., a film or solid component) made of EPDM adhered to (b) a second polymer structure (film or solid component) that is made of a blend of dynamically vulcanized EPDM dispersed in a matrix of a thermoplastic polyolefin polymer. Either the first polymer structure, or both the first and second polymer structures are blended with an effective amount of a semicrystalline random adhesive copolymer.