A hierarchical composite for use in energy dissipation applications has been studied. The composite is designed to combine three desirable properties: low weight, high strength and high energy absorption. This is accomplished by using two constituent materials with different cellular architectures: a periodic lattice for strength and a stochastic foam for energy absorption. The goals of the work presented here are to understand (i) how the two constituents behave on their own, and (ii) how they behave within the composite. X-ray computed microtomography was used to investigate the patial deformation of the two phases when the composite is compressed. Results from this study revealed that the foam phase stabilizes the lattices, delaying strut buckling, and increasing the flow stress of the system. The addition of foam doubles the energy absorption per unit volume of the lattice, while only increasing its density by 22%. This indicates that, under quasi-static compression, the system benefits from synergy between the two phases. This study highlights a possible route for achieving both strength and energy absorption in cellular materials.