In this study, a novel hybrid metamaterial has been developed via fulfilling hyperbolic chiral lattice with polyurethane (PU) foam. Initially, both the hyperbolic and typical body-centered cubic (BCC) lattices are fabricated by 3D printing technique. These lattices are infiltrated in a thermoplastic polyurethane (TPU) solution dissolved in 1,4-Dioxane, and then freeze casting technique is applied to achieve the PU-foam-filling. Intermediate (IM) layers possessing irregular pores, are formed neighboring to the lattice-foam interface. While, the foam far from the lattice exhibits a multi-layered structure. The mechanical behavior of the hybrid lattice metamaterials has been investigated by monotonic and cyclic compressive tests. The experimental monotonic tests indicate that, the filling foam is able to soften the BCC lattice but to stiffen the hyperbolic one, further to raise the stress plateau and to accelerate the densification for both lattices. The foam hybridization also benefits the hyperbolic lattice to prohibit the property degradation under the cyclic compression. Furthermore, the failure modes of the hybrid hyperbolic lattice are identified as the interface splitting and foam collapse via microscopic analysis. Finally, a parametric study has been performed to reveal the effects of different parameters on the compressive properties of the hybrid hyperbolic lattice metamaterial.