An electrical box assembly includes a cover assembly, a gasket and an electrical box coupled together by mounting screws. The cover includes a base with a plurality of screw holes for receiving the mounting screws. A support member having an axial passage extends from the bottom face of the cover around each of the screw holes. The gasket includes a cylindrical shaped sleeve that passes through the support member and has an axial length to extend from the screw hole in the cover. The mounting screws are inserted through the axial passage of the sleeve and the screw holes in the cover to axially compress the sleeve to form a watertight seal between the screw shaft and the support member.