Fullerene-based materials are widely used as electron acceptors in organic bulk-heterojunction solar cells; yet, they have rarely been used as the only photoactive component due to their low absorbance and limited charge generation efficiency. However, blending the wide-bandgap p-type material copper (I) thiocyanate (CuSCN) with [6,6]-phenyl-C71-butyric acid methyl ester (PC70BM) leads to the formation of a unique mesostructured p-n like heterointerface between CuSCN and PC70BM and solar cells with a power conversion efficiency (PCE) of up to 5.4%. Here, we examine in detail the reasons for the surprisingly good device performance and elucidate the charge photogeneration and recombination mechanisms in CuSCN-based devices with PC70BM as the exclusive light-absorbing material. Our studies clearly demonstrate that a substantial fraction of the photocurrent in the CuSCN-based devices results from improved dissociation of fullerene excitons and efficient charge transfer at the CuSCN:PC70BM interface combined with reduced geminate and nongeminate charge recombination losses. Our results have implications beyond the fullerene-based devices studied here, as they demonstrate that careful selection of a mesostructured p-type transparent semiconductor paves the path to a new type of efficient single photoactive material solar cells.