In this paper a spectrum-splitting photovoltaic system is proposed that uses bifacial silicon solar cells to maximize total energy yield. The system is unique in its ability to convert direct sunlight with high-efficiency (<30%) while simultaneously converting diffuse and rear-side irradiance. A volume holographic lens array is used to divide the solar spectrum into spectral bands optimized for conversion by wide-bandgap and bifacial silicon solar cells. An approach for simulating the energy yield, optimizing the holographic lens array, and analyzing the effect of concentration ratio, aspect ratio, and illumination characteristics is described. Design examples for two different solar cell combinations are provided. A GaAs and bifacial silicon combination achieves an energy conversion efficiency of 32.0% and a MgCdTe and bifacial silicon combination achieves a 31.0% energy conversion efficiency. Additional solutions are provided when constraints on concentration ratio and aspect ratio are applied, allowing the designer to balance energy yield with cost and size considerations. The performance of the proposed system is compared to conventional monofacial silicon, bifacial silicon, and monofacial spectrum-splitting modules, and show that improvements in energy yield of over 45%, 25%, and 10% can be achieved, respectively.