A "complex salt" of cetyltrimethylammonium (CTA(+)) with short (30 repeating units) polyacrylate (PA(-)) counterions has been synthesized. The phase diagrams of its aqueous mixtures with either the surfactant cetyltrimethylammonium acetate (CTAAc), or the polyelectrolyte NaPA, have been studied by visual inspection through crossed polarizers and by small-angle X-ray scattering. Both of the ternary phase diagrams are strikingly simple, containing only micellar, cubic micellar, and hexagonal phases. In the CTAPA/CTAAc/water system, the surfactant forms essentially spherical micelles above ca. 50 wt % of water, regardless of the counterion composition, and the system may serve as a model for charged colloids with mixed monovalent/polymeric counterions. The interactions between micelles varies from repulsive to attractive as the fraction of monovalent counterions is decreased. This results, first, in a liquid-liquid phase separation between a concentrated branch and a dilute branch of the micellar phase and, finally, a crystallization of micelles into a cubic (Pm3n) phase in equilibrium with essentially pure water. Small fractions of polymeric counterions "melt" the cubic phase. This is attributed to heterogeneity: A small proportion of micelle pairs that share polymeric counterions experience strong attractions. In CTAPA/NaPA/water mixtures, the micelle-micelle interactions switch from attractive to repulsive as the NaPA content is increased. A similar effect occurs with added NaAc. Monte Carlo simulations of interactions between surfactant aggregates neutralized by mixed polymeric and monovalent counterions qualitatively reproduce all experimental trends and show that the dominating source of the attraction between the aggregates is polyion bridging.