Transparent p-n heterojunction diodes are fabricated using p-type CuYO2:Ca and n-type ZnO:Al thin films on a glass substrate coated with indium-tin oxide (ITO). The contact between the n-ZnO:Al / p-CuYO2:Ca heterojunction is found to be rectifying, while the ITO / ZnO:Al contact is ohmic. The typical ratio of forward to reverse current is 15 in the range -3 to 3V. The diode current-voltage characteristics are dominated by the flow of space charge limited current, which is ascribed to the existence of an insulating ZnO interfacial layer. The diode structure has a total thickness of 0.85 μm and an optical transmission of 40%-50% in the visible region.