According to an aspect of the present invention, implantable or insertable medical devices are provided, which contain at least one polymeric region in contact with a metallic region. The polymeric region contains at least one block copolymer that contains at least one low Tg block and at least one high Tg block. The polymeric region contains at least one polymer that contains at least one adhesion promoting group selected from one or more of halo-silane, alkoxy-silane, epoxy, anhydride, phenoxy, hydroxyl, amino, sulfonate and carboxyl groups, which at least one polymer may correspond to the block copolymer, a supplemental polymer, or both.