Polymerization-induced self-assembly (PISA) is a polymerization process in which amphiphilic block copolymers are simultaneously synthesized and self-assembled in a selective solvent, leading to nanoparticles of different morphologies. Copolymerization has been reported as a means to tune morphology by changing the properties of the core block. Most examples in aqueous dispersed media are however limited to the copolymerization of hydrophobic monomers, while copolymerization between hydrophobic and hydrophilic/ionisable monomers has scarcely been reported. In this work, we study the aqueous PISA copolymerization of a mildly hydrophobic monomer (methoxyethylacrylate, MEA) with a hydrophilic pH-responsive monomer, acrylic acid (AA). Kinetic studies reveal that the incorporation of AA is strongly dependent on the pH at which the polymerization is performed: quasi-random copolymers form at low pH, whereas gradient composition profiles with lower AA contents are obtained at higher pH. The incorporation of AA, its degree of ionization, as well as its distribution in the copolymer chain (determined by the pH of the polymerization medium) strongly affect the particle morphology. Moreover, the amount and degree of ionization of AA, and the composition profile of the copolymer have a strong effect on the responsiveness of the particles post-polymerization, both to pH and to temperature. This work highlights that the incorporation of ionisable units within hydrophobic blocks by a typical aqueous PISA process strongly impacts their composition profile and, at the same time, provides a powerful tool to modify the morphology of the resulting nanoparticles.