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Inspired by the networked venation structures, a reinforced hourglass lattice structure is proposed to overcome the insufficient face-core interaction and premature face-sheet buckling that limit the compressive performance of conventional lattice sandwich structures. The reinforced hourglass lattice structure is fabricated using a cutting-interlocking assembly followed by vacuum brazing, enabling enhanced connectivity and increased effective contact area between the lattice core and the face sheets. Quasi-static in-plane and out-of-plane compression experiments, together with finite element simulations and theoretical analysis, are conducted to systematically investigate the compressive behavior of the reinforced hourglass lattice structure. The results demonstrate that the out-of-plane compressive strength of the reinforced hourglass lattice structure exhibits a pronounced dependence on relative density, increasing monotonically with increasing density. Under in-plane compression, comparative studies with conventional hourglass and pyramidal lattice structures reveal that the proposed reinforcement strategy significantly improves face-core load transfer and effectively suppresses local buckling of thin face sheets. As a consequence, the reinforced hourglass lattice structure exhibits higher initial stiffness, enhanced compressive strength, and superior structural stability. These findings indicate that reinforcing the reinforced hourglass core provides an effective design strategy for improving the compressive performance of lattice sandwich structures by strengthening face-core interaction and mitigating face-sheet buckling.