We have examined how the nanomorphology and crystallinity of semiconducting double-crystalline block copolymers determine their photophysical and photovoltaic responses. The block copolymers consist of a poly(3-hexylthiophene) (P3HT) donor block coupled to a polymerized perylene bisimide acrylate (PPerAcr) acceptor. Different molecular weights and processing solvents allow the modification of the donor-acceptor interface with regard to their morphology and crystallinity. Transient absorption spectroscopy was used to resolve photoinduced charge transfer seen on the similar to 1 ps time scale, consistent with substantial photoluminescence quenching caused by finely dispersed, disordered donor-acceptor interfaces. For high molecular weight block copolymers, microphase separation is enhanced by slow film formation, leading to slower charge photogeneration. The crystallinity of the P3HT component is of particular importance, which has been monitored spectroscopically. Crystalline P3HT/PPerAcr interfaces lead to high levels of long-lived charge pairs that are more easily extracted in an applied electric field. While external quantum efficiencies of over 25% were obtained, the overall power conversion efficiency of the best block copolymer device is still limited. This is due to the unsuitable orientation of the block copolymer nanomorphology, and the performance lies below that achieved for a blend of equivalent homopolymers. This suggests that increasing the molecular weight of the block copolymers to tune the microphase separation could further improve the photovoltaic efficiency. Our photophysical results give guidelines for future development of promising block copolymer derived devices, highlighting the importance of interfacial crystallinity and sufficient phase separation.