The phase behavior of metallo-supramolecular block copolymers with bulky counter ions is theoretically studied within the framework of a mean-field dynamic density functional theory and compared with recent experiments on a polystyrene-poly(ethylene oxide) metallo-supramolecular diblock copolymer, PS20-[Ru]-PEO70, with tetraphenylborate counter ions. The copolymer is modeled as a triblock polyelectrolyte, in which the metal complex is treated as the polyelectrolyte block. The topology and kinetics of the formation of the observed three-domain lamellar morphology in which the polyelectrolyte blocks and bulky counter ions are located together to form electroneutral complexes, are in good agreement with experimental results. In addition, the model predicts the existence of core-shell morphologies. The agreement with and variations from the experimental phase diagram are discussed in detail.