Vertical heterostructures of MoS2 and WSe2 layers are studied by spectroscopic photoemission electron microscopy as an effective technique for correlating chemical and electronic states at the micrometer scale. Element-specific, surface-sensitive images recorded at high lateral and energy resolution from core-level photoelectrons using different laboratory excitation sources are postprocessed to obtain laterally resolved maps of elemental composition and energy shifts in the Mo3d spectra of a few hundred meV. For monolayer MoS2, the method reveals substrate-dependent charge transfer properties within the narrow energy range of 360 meV, with MoS2 becoming more n-type after transfer onto WSe2. The band structure data from momentum microscopy taken over the same areas confirm the charge transfer from WSe2 to MoS2 by the shift of the K-bands away from the Fermi level and illustrates the layer-specific contributions to the electronic band structure of the heterostructure. From work function mapping, the reconstructed energy-level diagram reveals a type II heterostructure but with a very small conduction-band offset.