Carbon fiber reinforced polymer (CFRP) composites are known for their high stiffness-to-weight and high strength-to-weight ratios and hence are of great interest in several engineering fields such as aerospace, automotive and defense. However, despite their light weight, high stiffness and high strength, their application in these fields is limited due to their poor energy dissipation and vibration damping capabilities. This thesis presents a two-phase microlattice design to overcome this problem. To realize this design, a novel tape casting integrated multi-material stereolithography system is developed and mechanical properties of samples fabricated using this system are evaluated. The design incorporating a stiff phase (CFRP) and a high loss phase, exhibiting high stiffness as well as high damping, is studied via analytical and experimental approaches. To investigate its damping performance, mechanical properties at small-strain and large-strain regimes are measured through dynamic material analysis (DMA) and quasi-static cyclic compression tests respectively. It is seen that both intrinsic (small-strain) and structural (large-strain) damping in terms of a figure of merit (FOM), E1/3tanδ/ρ, can be enhanced by a small addition of a high loss phase in Reuss configuration. Moreover, it is seen that structural damping is improved at low relative densities due to the presence of elastic buckling during deformation. For design usefulness, tunability maps, displaying FOM in terms of design parameters, are developed by curve fitting of experimental measurements. The microlattice design is also evaluated quantitatively by comparing it with existing families of materials in a stiffness-loss map, which shows that the design is as stiff as commercial CFRP composites and as dissipative as elastomers.