Vertically stacked metal-semiconductor-metal heterostructures, based on liquid-processed nanomaterials, hold great potential for various printed electronic applications. Here we describe the fabrication of such devices by spray-coating semiconducting tungsten disulfide (WS2) nanosheets onto indium tin oxide (ITO) bottom electrodes, followed by spraying single-walled carbon nanotubes (SWNTs) as the top electrode. Depending on the formulation of the SWNTs ink, we could fabricate either Ohmic or Schottky contacts at the WS2/SWNTs interface. Using isopropanol-dispersed SWNTs led to Ohmic contacts and bulk-limited devices, characterized by out-of-plane conductivities of ∼10-4 S m-1. However, when aqueous SWNTs inks were used, rectification was observed, due to the formation of a doping-induced Schottky barrier at the WS2/SWNTs interface. For thin WS2 layers, such devices were characterized by a barrier height of ∼0.56 eV. However, increasing the WS2 film thickness led to increased series resistance, leading to a change-over from electrode-limited to bulk-limited behavior at a transition thickness of ∼2.6 μm. This work demonstrates that Ohmic/Schottky behavior is tunable and lays the foundation for fabricating large-area 2D nanosheet-based solution-deposited devices and stacks.