An electronic device may have a display and a rear housing. A coating may be formed on an inner surface of a display cover layer for the display or on an inner surface of the rear housing. The coating may include one or more inorganic layers such as inorganic layers in a thin-film interference filter or other layer of material. A buffer layer having a polymer with adhesion promotion additive and embedded silicon oxide particles may be interposed between the coating and a glass layer forming the rear housing or between a patterned indium tin oxide coating on a display cover layer and an adhesive layer that attaches a pixel array to the display cover layer.