In this study, a three-dimensional (3D) interconnected porous Ni/SiC skeleton (3D Ni/SiC) was synthesized by binder-free hydrogen bubble template-assisted electrodeposition in an electrolyte containing Ni²⁺ ions and SiC nanopowders. This 3D Ni/SiC skeleton served as a substrate for directly synthesizing nickel–cobalt layered double hydroxide (LDH) nanosheets via electrodeposition, allowing the formation of a nickel–cobalt LDH nanosheet-decorated 3D Ni/SiC skeleton (NiCo@3D Ni/SiC). The multiscale hierarchical structure of NiCo@3D Ni/SiC was attributed to the synergistic interaction between the pseudocapacitor (3D Ni skeleton and Ni–Co LDH) and electrochemical double-layer capacitor (SiC nanopowders). It provided a large specific surface area to expose numerous active Ni and Co sites for Faradaic redox reactions, resulting in an enhanced pseudocapacitance. The as-fabricated NiCo@3D Ni/SiC structure demonstrated excellent rate capability with a high areal capacitance of 1565 mF cm⁻² at a current density of 1 mA cm⁻². Additionally, symmetrical supercapacitor devices based on this structure successfully powered commercial light-emitting diodes, indicating the potential of as-fabricated NiCo@3D Ni/SiC in practical energy storage applications.