Lowering the driving voltage of organic light-emitting diodes (OLEDs) is an important approach to reduce their energy consumption. We have fabricated a series of bifunctional devices (OLEDs and photovoltaics) using rubrene and fullerene (C60) as the active layer, in which the electroluminescence threshold voltage(~1.1 V) was half the value of the bandgap of rubrene. Magneto-electroluminescence (MEL) response of planner heterojunction diodes exhibited a small increase in response to a low magnetic field strength (<20 mT); however, a very large decay was observed at a high magnetic field strength (>20 mT). When a hole-transport layer with a low mobility was included in these devices, the MEL response reversed in shape, and simultaneously, the EL threshold voltage became larger than the bandgap voltage. When bulk heterojunction device was examined, the amplitude of MEL curves presented an anomalous voltage-dependence. Following an analysis of the MEL responses of these devices, we proposed that the EL of half-bandgap-voltage device originated from bimolecular triplet-triplet annihilation in the rubrene film, rather than from singlet excitons that formed via an interface auger recombination. This work provides critical insight into the mechanisms of OLED emission and will help advance the applications of bifunctional devices.