We used sequential anionic living polymerization to synthesize poly(styrene-b-4-vinylpyridine) (PS-b-P4VP) and poly(vinylphenol-b-methyl methacrylate) (PVPh-b-PMMA) diblock copolymers presenting various hydrogen bond donor or acceptor units. Upon blending with the miscible disordered PVPh-b-PMMA diblock copolymers, we observed order-order morphological transitions from the bicontinuous gyroid structure of pure PS-b-P4VP to lamellar, cylindrical, and worm-like structures, in a manner strongly dependent on the concentration and vinylphenol content of the PVPh-b-PMMA diblock copolymer. We took advantage of competitive hydrogen-bonding interactions and Delta K effects between PVPh/P4VP and PVPh/PMMA domains when blending immiscible A-b-B diblock copolymers with disordered miscible C-b-D diblock copolymers to form hierarchical self-assembled nanostructures, including three-phase lamellar and core-shell cylindrical nanostructures.