We study the elastic moduli and structure of boron carbide/aluminum (B4C/Al) multiphase composites using rigorous bounding and experimental characterization techniques. We demonstrate that rigorous bounds on the effective moduli are useful in that they can accurately predict (i) the effective elastic moduli, given the phase moduli and volume fractions, or (ii) the phase moduli (volume fractions), given the effective moduli and phase volume fractions (moduli). Using the best available rigorous bounds on the effective elastic moduli of multiphase composites involving volume-fraction information, we are able to predict the bulk and shear moduli of the AI,BC phase, a reaction product that forms during heat treatment. These theoretical predictions are in very good agreement with recent experimental measurements of the moduli of the AI,BC phase. Moreover, we evaluate more-refined bounds involving three-point structural correlation functions by extracting such information from an image of a sample of the B4C/Al composite. Although experimental data for the effective moduli are unavailable for this sample, our predictions of the effective moduli based on three-point bounds should be quite accurate.