Electrostatics plays a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can co-assembled into functional units, such as DNA and histone proteins into nucleosomes and actin-binding protein complexes into cytoskeleton components, at appropriate ionic conditions. These cationic-anionic co-assemblies often have surface charge heterogeneities that result from the delicate balance between electrostatics and packing constraints. Despite their importance, the precise role of surface charge heterogeneities in the organization of cationic-anionic co-assemblies is not well understood. We show here that co-assemblies with charge heterogeneities strongly interact through polarization of the domains. We find that this leads to symmetry breaking, which is important for functional capabilities, and structural changes, which is crucial in the organization of co-assemblies. We determine the range and strength of the attraction as a function of the competition between the steric and hydrophobic constraints and electrostatic interactions.