Through controlled annealing of planar heterojunction (bilayer) devices based on the polyfluorene copolymers poly(9,9-dioctylfluorene-co-bis(N,N'-(4, butylphenyl))bis(N,N'-phenyl-1,4-phenylene)diamine) (PFB) and poly(9,9-dioctylfluorene-co-benzothiadiazole) (F8BT) we study the influence of interface roughness on the generation and separation of electron-hole pairs at the donor/acceptor interface. Interface structure is independently characterized by resonant soft X-ray reflectivity with the interfacial width of the PFB/F8BT heterojunction observed to systematically increase with annealing temperature from 1.6 nm for unannealed films to 16 nm with annealing at 200 degrees C for ten minutes. Photoluminescence quenching measurements confirm the increase in interface area by the three-fold increase in the number of excitons dissociated. Under short-circuit conditions, however, unannealed devices with the sharpest interface are found to give the best device performance, despite the increase in interfacial area (and hence the number of excitons dissociated) in annealed devices. The decrease in device efficiency with annealing is attributed to decreased interfacial charge separation efficiency, partly due to a decrease in the bulk mobility of the constituent materials upon annealing but also (and significantly) due to the increased interface roughness. We present results of Monte Carlo simulations that demonstrate that increased interface roughness leads to lower charge separation efficiency, and are able to reproduce the experimental current-voltage curves taking both increased interfacial roughness and decreased carrier mobility into account. Our results show that organic photovoltaic performance can be sensitive to interfacial order, and heterojunction sharpness should be considered a requirement for high performance devices.