Skin-inspired soft and stretchable electronic devices based on functional nanomaterials have broad applications such as health monitoring, human-machine interface, and the Internet of things. Solution-processed conductive nanocomposites have shown great promise as a building block of soft and stretchable electronic devices. However, realizing conductive nanocomposites with high conductivity, electromechanical stability, and low modulus over a large area at sub-100 μm resolution remains challenging. Here, we report a moldable, transferrable, high-performance conductive nanocomposite comprised of an interpenetrating network of silver nanowires and poly(3,4-ethylenedioxythiophene): poly(styrenesulfonate). The stacked structure of the nanocomposite synergistically integrates the complementary electrical and mechanical properties of the individual components. We patterned the nanocomposite via a simple, low-cost micromolding process and then transferred the patterned large-area electrodes onto various substrates to realize soft, skin-interfaced electrophysiological sensors. Electrophysiological signals measured using the nanocomposite electrodes exhibit a higher signal-to-noise ratio than standard gel electrodes. The nanocomposite design and fabrication approach presented here can be broadly employed for soft and stretchable electronic devices.