We report the synthesis and photophysical characterization of a series of hexa-peri-hexabenzocoronene (HBC)/perylenetetracarboxy diimide (PDI) dyads that are covalently linked with a rigid bridge. Both the ratio of the two components and the conjugation of the bridging element are systematically modified to study the influence on self-assembly and energy and electron transfer between electron donor HBC and acceptor PDI. STM and 2D-WAXS experiments reveal that both in solution and in bulk solid state the dyads assemble into well-ordered two-dimensional supramolecular structures with controllable mutual orientations and distances between donor and acceptor at a nanoscopic scale. Depending on the symmetry of the dyads, either columns with nanosegregated stacks of HBC and PDI or interdigitating networks with alternating HBC and PDI moieties are observed. UV-vis, photoluminescence, transient photoluminescence, and transient absorption spectroscopy confirm that after photoexcitation of the donor HBC a photoinduced electron transfer between HBC and PDI can only compete with the dominant Förster resonance energy transfer, if facilitated by an intimate stacking of HBC and PDI with sufficient orbital overlap. However, while the alternating stacks allow efficient electron transfer, only the nanosegregated stacks provide charge transport channels in bulk state that are a prerequisite for application as active components in thin film electronic devices. These results have important implications for the further design of functional donor-acceptor dyads, being promising materials for organic bulk heterojunction solar cells and field-effect transistors.