Block copolymers have the unique property to self-assemble into ordered microstructures with well-defined periodicity. Among the various attainable microdomain morphologies, complex morphologies with inherent structural connectivity are highly desirable. While such structures are difficult to obtain in monodisperse block copolymers, they may be stabilized by increasing block dispersity. In this study, we prepare poly (styrene-b-methyl methacrylate) (PS-b-PMMA) diblock copolymers where dispersity of both PS and PMMA blocks are varied independently. Morphology examination of the diblocks reveals that at fixed block composition, dispersity dictated phase transition is observed. In particular, in the case where dispersity of both blocks are high, the polymers are found to exhibit perforated lamellae and disordered bicontinuous morphologies. Dissipative particle dynamics (DPD) simulations are also carried out to confirm the stability of the observed morphologies. These results show that control of block dispersity can effectively stabilize energetically disfavored complex morphologies in block copolymers.