Despite having several advantages, bicontinuously structured polymeric nanoparticles (BSPNPs) are far less explored in the field of controlled drug delivery owing to the requirement of complex precursor copolymers and the associated multistep synthetic procedures. In this work, we report the synthesis of a redox-sensitive diblock copolymer (P1), which was subsequently utilized to prepare doxorubicin (DOX) containing a pH-labile prodrug (P2). P1 and P2 spontaneously self-assembled in aqueous media above their critical aggregation concentration, forming micellar nanoparticles with rare bicontinuous morphology that promotes loading of both hydrophobic and hydrophilic cargoes in different compartments. To the best of our knowledge, the formation of BSPNPs through direct self-assembly in aqueous media has not yet been reported. In vitro cellular studies asserted the higher safety profile of the nanoparticles against noncancerous cells (HEK293T) than free DOX, whereas they displayed higher drug-induced cytotoxicity against cancer cells (MCF-7) in comparison to free DOX, establishing them as promising cancer drug delivery systems.