The mesoscopic morphology of binary mixtures of ethylammonium nitrate (EAN), the protic ionic liquid par excellence, and methanol is explored using neutron/X-ray diffraction and computational techniques. Both compounds are amphiphilic and characterized by an extended hydrogen bonding network: surprisingly, though macroscopically homogeneous, these mixtures turn out to be mesoscopically highly heterogeneous. Our study reveals that even in methanol-rich mixtures, a wide distribution of clusters exists where EAN preserves its bulk, sponge-like morphology. Accordingly methanol does not succeed in fully dissociating the ionic liquid that keeps on organizing in a bulk-like fashion. This behavior represents the premises to the more dramatic phenomenology observed with longer alcohols that eventually phase separate from EAN. These results challenge the commonly accepted polar and apolar moieties segregation in ionic liquids/molecular liquids mixtures and the current understanding of technologically relevant solvation processes.