Solid electrolytes, as a promising replacement for the flammable liquid electrolyte in conventional Li-ion batteries, may greatly alleviate the safety issues and improve the energy density. However, mainstream electrodes are also solid. If solid electrolytes were employed, creating intimate electrode-electrolyte contact similar to that between solid and liquid would be quite difficult. Here we discovered that, by forming epitaxial interfaces, such a seamless solid-solid contact can happen between two widely studied systems: the Li-rich layered electrode and perovskite solid electrolyte. Atomic-resolution electron microscopy unambiguously demonstrated that the former can be epitaxially embedded into the latter. The solid-solid composite electrode formed this way exhibited a rate capability no lower than the one based on solid-liquid contact. With the periodic misfit dislocations reconciling structural differences, such epitaxy can tolerate large lattice mismatch, and thus may occur between many layered electrodes and perovskite solid electrolytes