Cobaltite systems with spinel structures are promising cathode materials for next-generation high-performance electrochemical capacitors because of their high electrochemical stability. However, increasing the mass loading of active materials without sacrificing the geometry of the nanostructures remains a challenge. In this study, we propose vertically stacked bilayer spinel heterostructures constructed from hierarchical CuCo₂O₄/MnCo₂O₄ on graphite paper as highly capable supercapacitor electrodes. A two-step hydrothermal method with post annealing treatment is used in the preparation of the heterostructures. The CuCo₂O₄/MnCo₂O₄ electrode delivers a remarkable specific capacitance of 1434 F g⁻¹ at 0.5 A g⁻¹, considerable high-rate capability (810 F g⁻¹ at 15 A g⁻¹), and an excellent cycling stability, maintaining 81.4% at 10 A g⁻¹ after 5000 cycles. An electrochemical capacitor device operating at 1.6 V is also constructed using CuCo₂O₄/MnCo₂O₄ and graphene as positive and negative electrodes, respectively. The device shows a high energy density of 42.1 W h kg⁻¹ at a power density of 400 W kg⁻¹, as well as good cycling stability (88.4% retention after 10 000 cycles). The concept of stacking heteronanostructures can potentially enrich the electrochemical performance of metal oxides for next-generation electrochemical capacitors.