A coupled modeling and experimental investigation of the mechanical response of a dual-phase composite ceramic is reported. The material consists of boron carbide crystals interspersed with a second phase of titanium diboride, where grains of each phase are of comparable average size. Experiments show a moderate increase in flexure strength and a significant increase in fracture toughness with increasing titanium diboride content. Density functional theory provides elastic properties, surface energy on potential cleavage planes, and stacking fault energy on potential slip systems of the second phase. Energies are found lowest on the basal plane. Findings inform mesoscale simulations of the tensile response of polycrystalline aggregates. These simulations, which invoke a phase-field theory for elasticity, limited slip, and fracture, demonstrate improvement in tensile strength with increasing fraction of titanium diboride grains, in qualitative agreement with experimental trends. Refinements are suggested that would presumably provide more accurate toughness predictions.