Hybrid solid electrolytes, composed of 3D ordered bicontinuous conducting ceramic and insulating polymer microchannels are reported. The ceramic channels provide continuous, uninterrupted pathways, maintaining high ionic conductivity between the electrodes, while the polymer channels permit improvement of the mechanical properties from that of the ceramic alone, in particular mitigation of the ceramic brittleness. The conductivity of a ceramic electrolyte is usually limited by resistance at the grain boundaries, necessitating dense ceramics. The conductivity of the 3D ordered hybrid is reduced by only the volume fraction occupied by the ceramic, demonstrating that the ceramic channels can be sintered to high density similar to a dense ceramic disk. The hybrid electrolytes are demonstrated using the ceramic lithium ion conductor Li1.4Al0.4Ge1.6(PO4)3 (LAGP). Structured LAGP 3D scaffolds with empty channels were prepared by negative replication of a 3D printed polymer template. Filling the empty channels with non-conducting polypropylene (PP) or epoxy polymer (epoxy) creates the structured hybrid electrolytes with 3D bicontinuous ceramic and polymer microchannels. Printed templating permits precise control of the ceramic to polymer ratio and the microarchitecture; as demonstrated by the formation of cubic, gyroidal, diamond and spinodal (bijel) structures. The electrical and mechanical properties depend on the microarchitecture, the gyroid filled with epoxy giving the best combination of conductivity and mechanical properties. An ionic conductivity of 1.6 × 10−4 S cm−1 at room temperature was obtained, reduced from the conductivity of a sintered LAGP pellet only by the volume fraction occupied by the ceramic. The mechanical properties of the gyroid LAGP–epoxy electrolyte demonstrate up to 28% higher compressive failure strain and up to five times the flexural failure strain of a LAGP pellet before rupture. Notably, this demonstrates that ordered ceramic and polymer hybrid electrolytes can have superior mechanical properties without significantly compromising ionic conductivity, which addresses one of the key challenges for all-solid-state batteries.