An electronic device has a display mounted in a housing using a plastic display frame. The display has an active area and an inactive area. A display cover layer may have polymer coating layers in the inactive area. The display frame may lie under the inactive area. A patterned metal coating layer may be formed on the display frame. The patterned metal coating layer may have portions that form adhesion promotion structures for promoting adhesion between the frame and the adhesive. The patterned metal coating layer may also have portions that form antenna structures. The antenna structures may be used to transmit and receive radio-frequency signals and may be used as adhesion promotion structures. Adhesive may be interposed between the polymer coating layers and the metal coating layer on the display frame to attach the display cover layer and the display to the display frame.