Mechanical metamaterials can achieve high stiffness and strength at low densities, but often at the expense of low ductility and stretchability—a persistent trade-off in materials. In contrast, double-network hydrogels feature interpenetrating compliant and stiff polymer networks, and exhibit unprecedented combinations of high stiffness and stretchability, resulting in exceptional toughness. Here we present double-network-inspired metamaterials by integrating monolithic truss (stiff) and woven (compliant) components into a metamaterial architecture, which achieves a tenfold increase in stiffness and stretchability compared to its pure counterparts. Nonlinear computational mechanics models elucidate that enhanced energy dissipation in these double-network-inspired metamaterials stems from increased frictional dissipation due to entanglements between networks. Through introduction of internal defects, which typically degrade mechanical properties, we demonstrate a threefold increase in energy dissipation for these metamaterials via failure delocalization. This work opens avenues for developing metamaterials in a high-compliance regime inspired by polymer network topologies.