The efficiency of dye-sensitized solar cells may be further improved if ways are found to broaden the spectral response resolving the fundamental issues involved. Here we report construction of dye-sensitized solid-state photovoltaic cells with heterostructure configurations: [1] n-TiO2/D-1/p-CuSCN, M n-TiO2/p-CuSCN/D-2/ p-CuSCN and [3] n-TiO2/D-1/p-CuSCN/D-2/P-CuSCN, where n-TiO2 is a similar to10 mum thick nanocrystalline film of titanium dioxide, p-CuSCN and p-CuSCN are thin (similar to 2 nm) and thick (similar to 10 mum) films of copper(I) thiocyanate. Monolayers of the dyes D-1 (Fast Green) and D-2 (Acridine Yellow) are coated on TiO2 and p-CuSCN, respectively. The cell of configuration [3] delivered the highest efficiency, open-circuit voltage, and short-circuit photocurrent as it effectively utilizes the light adsorbed by D-1 and D-2. The mechanism of operation involves tunneling of energetic electrons and holes liberated in photoexcitations of dyes through a thin barrier of p-CuSCN. The strategy adopted indicates the possibility of designing more efficient dye-sensitized solar cells, widening the spectral response.