Interfaces play a crucial role in composite magnetic materials and particularly in bimagnetic core/shell nanoparticles. However, resolving the microscopic magnetic structure of these nanoparticles is rather complex. Here, we investigate the local magnetization of antiferromagnetic/ferrimagnetic FeO/Fe3O4 core/shell nanocubes by electron magnetic circular dichroism (EMCD). The electron energy-loss spectroscopy (EELS) compositional analysis of the samples shows the presence of an oxidation gradient at the interface between the FeO core and the Fe3O4 shell. The EMCD measurements show that the nanoparticles are composed of four different zones with distinct magnetic moment in a concentric, onion-type, structure. These magnetic areas correlate spatially with the oxidation and composition gradient with the magnetic moment being largest at the surface and decreasing toward the core. The results show that the combination of EELS compositional mapping and EMCD can provide very valuable information on the inner magnetic structure and its correlation to the microstructure of magnetic nanoparticles.