We describe photoluminescence (PL), PL excitation, and time-resolved PL spectroscopy of hetero-bilayers comprising monolayers (1L) of MoS2 and MoSe2 at cryogenic temperatures. A PL peak showing a decay time of 2.5 ns was observed below 100 K, which can be attributed to an inter-layer exciton emission in the 1L-MoS2/1L-MoSe2 hetero-bilayers. An inter-layer exciton binding energy of similar to 90 meV is determined from its thermal dissociation behavior; the band offset of each layer obtained from this value is consistent with previously reported first-principles calculations. Moreover, generation of inter-layer charged excitons (trions) is implied from the gate modulation of the inter-layer exciton PL spectra.