Hydrophilicity of electrodes and minimal resistive losses are among of the most crucial parameters for designing an efficient asymmetric supercapacitor for aqueous systems. In this work, we present how MnO2 and MoS2 thin film based heterostructures fabricated onto the free-standing carbon nanotube sheets (CNTs) meet these conditions and offer high performance. Owing to the work function contrast between MoS2 and MnO2, we explore the maximum potential window in our asymmetric design. The self-standing electrodes are first tested in a three-electrode configuration, providing very high areal capacitance of 0.41 and 0.6 F cm−2, for MoS2/CNT and MnO2/CNT, respectively. MoS2/CNT electrode depicts purely electrostatic polarization in the voltage range of −0.6 to 0.2 V, whereas MnO2/CNT electrode also displays non-faradaic charge storage in the range of 0–1 V. Next, the device is fabricated and tested in a wide potential range from −0.6 to 1 V, with the calculated areal capacitance and volumetric capacitance of 0.34 F cm−2 and 6.5 F cm−3, respectively, with high coulombic efficiency of 82.3%. The scalable manufacturing technique involving a unique combination of chemical and physical deposition techniques gives hierarchical core-shell heterostructure consisting of large number of edge-exposed catalytic sites available for electrode-electrolyte interaction.