We report mechanically robust, electrically conductive, free-standing, and transparent hybrid nanomembranes made of densified carbon nanotube sheets that were coated with poly(3,4-ethylenedioxythiophene) using vapor phase polymerization and their performance as supercapacitors. The hybrid nanomembranes with thickness of ∼66 nm and low areal density of ∼15 μg/cm2exhibited high mechanical strength and modulus of 135 MPa and 12.6 GPa, respectively. They also had remarkable shape recovery ability in liquid and at the liquid/air interface unlike previous carbon nanotube sheets. The hybrid nanomembrane attached on a current collector had volumetric capacitance of ∼40 F/cm3 at 100 V s–1 (∼40 and ∼80 times larger than that of onion-like carbon measured at 100 V s–1 and activated carbon measured at 20 V s–1, respectively), and it showed rectangular shapes of cyclic voltammograms up to ∼5 V s–1. High mechanical strength and flexibility of the hybrid nanomembrane enabled twisting it into microsupercapacitor yarns with diameters of ∼30 μm. The yarn supercapacitor showed stable cycling performance without a metal current collector, and its capacitance decrease was only ∼6% after 5000 cycles. Volumetric energy and power density of the hybrid nanomembrane was ∼70 mWh cm–3 and ∼7910 W cm–3, and the yarn possessed the energy and power density of ∼47 mWh cm–3 and ∼538 W cm–3.