An electronic device may have a display cover layer mounted to a metal housing. Electrical component layers such as a display layer, touch sensor layer, and near-field communications antenna layer may be mounted under the display cover layer. An antenna feed may have a positive feed terminal coupled to the electrical component layers and a ground feed terminal coupled to the metal housing. The electrical component layers may serve as an antenna resonating element for an antenna. The antenna may cover cellular telephone bands and may receive satellite navigation system signals. A system-in-package device may be mounted to the metal housing. A flexible printed circuit may extend between the electrical component layers and the system-in-package device. A mounting bracket for the system-in-package device may be provided with electrical isolation to enhance antenna performance in bands such as a satellite navigation system band.