The resistive random access memory (RRAM) devices with heterostuctures have been investigated due to cycling stability, nonlinear switching, complementary resistive switching and self-compliance. The heterostructured devices can modulate the resistive switching (RS) behavior appropriately by bilayer structure with a variety of materials. In this study, the bipolar resistive switching characteristics of the bilayer structures composed of Ta2O5 and Ag2Se, which are transition-metal oxide (TMO) and silver chalcogenide, were investigated. The bilayer devices of Ta2O5 deposited on Ag2Se (Ta2O5/Ag2Se) and Ag2Se deposited on Ta2O5 (Ag2Se/Ta2O5) were fabricated for investigation of the RS characteristics by stacking sequence of Ta2O5 and Ag2Se. All operating voltages were applied to the Ag top electrode with the Pt bottom electrode grounded. The Ta2O5/Ag2Se device showed that a negative voltage sweep switched the device from high resistance state (HRS) to low resistance state (LRS) and a positive voltage sweep switched the device from LRS to HRS. On the contrary, for the Ag2Se/Ta2O5 device a positive voltage sweep switched the device from HRS to LRS, and a negative voltage sweep switched it from LRS to HRS. The polarity dependence of RS was attributed to the stacking sequence of Ta2O5 and Ag2Se. In addition, the combined heterostructured device of both bilayer stacks, Ta2O5/Ag2Se and Ag2Se/Ta2O5, exhibited the complementary switching characteristics. By using threshold switching devices, sneak path leakage can be reduced without additional selectors. The bilayer heterostructures of Ta2O5 and Ag2Se have various advantages such as self-compliance, reproducibility and forming-free stable RS. It confirms the possible applications of TMO and silver chalcogenide heterostructures in RRAM.