An electrical assembly including a first element, such as a connector body, formed of a conductive composite material and a second element formed of a solid metallic material, such as a sheet metal electromagnetic interference shield, defining a fibrous conductive region formed of a plurality of metallic filaments. The conductive composite material forming the first element completely surrounds a portion of the fibrous conductive region. Conductive fibers in the conductive composite material are in intimate contact with the fibrous conductive region, forming a very high number of electrical contact points between the conductive fibers in the conductive composite material and the fibrous conductive region and thereby providing a robust electrical connection between the first element and the second element.