We use electron transport to characterize monolayer graphene - multilayer MoS2 heterostructures. Our samples show ambipolar characteristics and conductivity saturation on the electron branch which signals the onset of MoS2 conduction band population. Surprisingly, the carrier density in graphene decreases with gate bias once MoS2 is populated, demonstrating negative compressibility in MoS2. We are able to interpret our measurements quantitatively by accounting for disorder and using the random phase approximation (RPA) for the exchange and correlation energies of both Dirac and parabolic-band two-dimensional electron gases. This interpretation allows us to extract the energetic offset between the conduction band edge of MoS2 and the Dirac point of graphene.