Visible light emission was observed for molecular junctions containing 5-19 nm thick layers of aromatic molecules between carbon contacts and correlated with their current-voltage behaviors. Their emission was compared to that from Al/AlOx/Au tunnel junctions, which has been previously attributed to transport of carriers across the AlOx layer to yield hot carriers which emit light as they relax within the Au contact. The maximum emitted photon energy is equal to the applied bias for the case of coherent tunneling, and such behavior was observed for light emission from AlOx and thin (<5 nm) molecular junctions. For thicker films, the highest energy observed for emitted photons is less than eVapp and exhibits an energy loss that is strongly dependent on molecular layer structure and thickness. For the case of nitroazobenzene junctions, the energy loss is linear with the molecular layer thickness, with a slope of 0.31 eV/nm. Energy loss rules out coherent tunneling as a transport mechanism in the thicker films and provides a direct measure of the electron energy after it traverses the molecular layer. The transition from elastic transport in thin films to lossy transport in thick films confirms that electron hopping is involved in transport and may provide a means to distinguish between various hopping mechanisms, such as activated electron transport, variable range hopping, and Poole Frankel transport.