Electrostatics play a key role in biomolecular assembly. Oppositely charged biomolecules, for instance, can be coassembled 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 coassemblies 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 coassemblies is not well understood. We show here that coassemblies 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 coassemblies. We determine the range and strength of the attraction as a function of the competition between the steric and hydrophobic constraints and electrostatic interactions.