Amphiphilic nucleobase-containing block copolymers with poly(oligo(ethylene glycol) methyl ether methacrylate) as the hydrophilic block and nucleobase-containing blocks as the hydrophobic segments were successfully synthesized using RAFT polymerization and then self-assembled via solvent switch in aqueous solutions. Effects of the common solvent on the resultant morphologies of the adenine (A) and thymine (T) homopolymers, and A/T copolymer blocks and blends were investigated. These studies highlighted that depending on the identity of the common solvent, DMF or DMSO, spherical micelles or bicontinuous micelles were obtained. We propose that this is due to the presence of A–T interactions playing a key role in the morphology and stability of the resultant nanoparticles, which resulted in a distinct system compared to individual adenine or thymine polymers. Finally, the effects of annealing on the self-assemblies were explored. It was found that annealing could lead to better-defined spherical micelles and induce a morphology transition from bicontinuous micelles to onion-like vesicles, which was considered to occur due to a structural rearrangement of complementary nucleobase interactions resulting from the annealing process.