An electronic device or other equipment may include an infrared-transparent one-way mirror. The infrared-transparent one-way mirror may be formed by a layer of material that is supported by a head-mounted support structure or other support structure. The support structure may support the layer of material so that the layer of material separates an exterior region from an interior region. Optical components in the interior region may be overlapped by the layer of material. The optical components may include visible light components such as a visible light camera and infrared components such as an infrared light-emitting device and an infrared light sensor. The optical components may operate through the layer of material while being hidden from view by the reflective appearance of the one way mirror from the exterior region.