Semiconductor heterostructures provide a powerful platform to engineer the dynamics of excitons for fundamental and applied interests. However, the functionality of conventional semiconductor heterostructures is often limited by inefficient charge transfer across interfaces due to the interfacial imperfection caused by lattice mismatch. Here we demonstrate that MoS2/WS2 heterostructures consisting of monolayer MoS2 and WS2 stacked in the vertical direction can enable equally efficient interlayer exciton relaxation regardless the epitaxy and orientation of the stacking. This is manifested by a similar 2 orders of magnitude decrease of photoluminescence intensity in both epitaxial and nonepitaxial MoS2/WS2 heterostructures. Both heterostructures also show similarly improved absorption beyond the simple superimposition of the absorptions of monolayer MoS2 and WS2. Our result indicates that 2D heterostructures bear significant implications for the development of photonic devices, in particular those requesting efficient exciton separation and strong light absorption, such as solar cells, photodetectors, modulators, and photocatalysts. It also suggests that the simple stacking of dissimilar 2D materials with random orientations is a viable strategy to fabricate complex functional 2D heterostructures, which would show similar optical functionality as the counterpart with perfect epitaxy.