A predictive molecular-thermodynamic theory is developed to model the effect of counterion binding on micellar solution properties of binary surfactant mixtures of ionic and nonionic (or zwitterionic) surfactants. The theory combines a molecular-thermodynamic description of micellization in binary surfactant mixtures with a recently developed model of counterion binding to single-component ionic surfactant micelles. The thermodynamic component of the theory models the equilibrium between the surfactant monomers, the counterions, and the mixed micelles. The molecular component of the theory models the various contributions to the free-energy change associated with forming a mixed micelle from ionic surfactants, nonionic (or zwitterionic) surfactants, and bound counterions (referred to as the free energy of mixed micellization). Specifically, the various molecular contributions to the free energy of mixed micellization model the underlying physics associated with the assembly of, and the interactions between, the surfactant polar heads, the surfactant nonpolar tails, and the bound counterions. Utilizing known structural characteristics of the surfactants and the counterions, along with the solution conditions, the free energy of mixed micellization is minimized to predict various optimal micelle characteristics, including the degree of counterion binding, the micelle composition, and the micelle shape and size. These predicted optimal micelle characteristics are then used to predict the critical micelle concentration (cmc) and the average micelle aggregation number. Our predictions of the degree of counterion binding, the cmc, and the average micelle aggregation number show good agreement with available experimental results from the literature for several binary surfactant mixtures. In addition, the theory is used to shed light on the relationship between the micelle composition, counterion binding and ion condensation, and the micelle shape transition.