We describe here the quasi-static crushing behavior of novel classes of multiphase (hybrid) hierarchical lattice metamaterials. The first class is represented by a hybrid architecture combining a hierarchical honeycomb with polyurethane foam filler, while the second is a multiphase structure produced by injecting an alginate hydrogel into the hierarchical voids of the honeycomb metamaterial. Twelve different auxetic (i.e. negative Poisson's ratio) and non-auxetic metamaterial architectures have been 3D printed and subjected to edgewise compression crushing loading. A parametric numerical analysis has been also performed using validated finite element models to identify best metamaterial architecture configurations. Configurations filled with the hydrogel showed a significant stabilization of the deformation mechanism during large deformation edgewise compression. The use of metamaterials designs with internal slots and round in the ribs also filled by polyurethane rigid semi-reticulated foam feature however significant increases in terms of specific stiffness, mean crushing force, strength and energy absorption. The enhancement is particularly evident for the hybrid lattice metamaterials auxetic configurations.