Hybrid micro-architected materials with unique combinations of high stiffness, high damping, and low density are presented. We demonstrate a scalable manufacturing pro- cess to fabricate hollow microlattices with a sandwich wall architecture comprising an elastomeric core and metallic skins. In this configuration, the metallic skins provide stiff- ness and strength, whereas the elastomeric core provides constrained-layer damping. This damping mechanism is effective under any strain amplitude, and at any relative den- sity, in stark contrast with the structural damping mechanism exhibited by ultralight metallic or ceramic architected materials, which requires large strain and densities lower than a fraction of a percent. We present an analytical model for stiffness and constrained-layer damping of hybrid hollow microlattices, and verify it with finite ele- ments simulations and experimental measurements. Subsequently, this model is adopted in optimal design studies to identify hybrid microlattice geometries which provide ideal combinations of high stiffness and damping and low density. Finally, a previously derived analytical model for structural damping of ultralight metallic microlattices is extended to hybrid lattices and used to show that ultralight hybrid designs are more efficient than purely metallic ones.