Achieving isotropic electrical and mechanical properties is essential for skin-integrated electronics to operate reliably under complex, multidirectional skin deformations. However, nanomaterial-based composites in skin electronics often rely on anisotropic filler configurations to meet demanding requirements for high-quality bio-interfacing materials, such as ultrathin thickness, high conductivity, and stretchability. While directional alignment of high-aspect-ratio nanofillers facilitates dense percolation, it compromises isotropic material uniformity. To overcome the trade-off between high performance and omnidirectional material properties in the nanocomposites, a controlled assembly strategy is proposed for silver nanosheets (AgNSs) that forms face-to-face contacts with partial overlaps, enhancing inter-sheet contact area and reducing contact resistance. Implementing this assembly configuration in an ultrathin elastomeric membrane yields a silver nanosheet nanomembrane (AgNS NM) with both isotropic material properties and high performance, featuring a high conductivity of ≈115 000 S cm^-1, a stretchability of ≈50%, and a total thickness of ≈235 nm. Coarse-grained molecular dynamics simulations (CGMD) reveal that the degree of overlap correlates with nanosheet geometry, providing design insights for controlling interfacial contact configurations in nanomaterials. Finally, the potential of the AgNS NM for bio-interfacing applications is demonstrated through an electrical impedance tomography-based tactile electronic skin, enabling reliable multi-point pressure mapping and real-time tracking.