Three-dimensional lattice-based Monte Carlo simulations of mixed amphiphile systems are investigated, and the simulated critical micelle concentrations (cmc's) are compared with the predictions of both a molecular thermodynamic theory and a regular solution theory. The head-head interactions between identical surfactant species are varied to mimic nonideal mixing and to manipulate the net attraction (or repulsion) between surfactant species. The simulations indicate that the head-head interaction affects not only the cmc but also aggregate size and structure. The simulated cmc as a function of overall surfactant composition is in reasonable agreement with the theoretical models when a fitted value for the interaction parameter, beta, is used. The fitted value is in good agreement with a value estimated a priori from the lattice model for the surfactants with attractive headgroups, but there are large discrepancies for the case of repulsive headgroups. The discrepancies in the latter are caused by nonrandom mixing, that is, segregation of the two surfactants within each micelle.