We study the influence of block copolymer (BCP) compatibilizers on the domain and interfacial characteristics of the equilibrium morphological structures of semiflexible polymer/solvent blends. Our study is motivated by the question of whether block copolymer compatibilizers can be used to influence the phase separation morphologies resulting in conjugated polymer/fullerene blends. Toward this objective, we use a single chain in mean field Monte Carlo simulations for the phase behavior of semiflexible polymer/solvent blends and study the influence of BCP compatibilizers on the morphologies. Our results reveal a range of blend compositions and molecular chemistries that result in equilibrium structures with domain sizes on the order of 5-20 nm. To elucidate the morphological characteristics of these structures, we first present a series of ternary phase diagrams and then present results demonstrating that the blend composition, semiflexible chain rigidity, BCP composition, and component miscibility each provide unique handles to control the phase separation morphologies and interfacial characteristics in such blends.