In organic semiconductor devices, the deposition of organic layers may result in intermixed regions or rough interfaces between layers. To examine how roughness at organic-organic interfaces influences device performance, we conducted mesoscopic device simulations using a three-dimensional kinetic Monte Carlo algorithm. We simulated devices containing interfaces with periodic corrugation of either triangular or rectangular cross section. Our results show how the shape and size of interfacial roughness impacts on both charge and exciton dynamics of unipolar and bipolar devices. We first analyzed bilayer devices where the two layers are energetically offset. We find interfaces with triangular cross section display strong carrier funneling to the tips. This funneling translates to pronounced inhomogeneity in the spatial distribution of charge carriers, excitons, and excitonic losses. The tips act as injection hot spots, increasing the current density by up to two orders of magnitude, depending on the energy offset, compared to a flat-interface device. In contrast, the internal quantum efficiency of bipolar devices is surprisingly unaffected by interfacial morphology. In bipolar three-layer devices, we used this enhancement in current density to improve charge injection toward the central emissive layer. The recombination zone within the emissive layer can also be tuned through the configuration and size of the morphology.