We present a computer simulation molecular-thermodynamic (CSMT) framework to model the micellization behavior of mixtures of surfactants in which hydration information from allatomistic simulations of surfactant mixed micelles and monomers in aqueous solution is incorporated into a well-established molecular-thermodynamic framework for mixed surfactant micellization. In addition, we address the challenges associated with the practical implementation of the CSMT framework by formulating a simpler mixture CSMT model based on a composition-weighted average approach involving single-component micelle simulations of the mixture constituents. We show that the simpler mixture CSMT model works well for all of the binary surfactant mixtures considered, except for those containing alkyl ethoxylate surfactants, and rationalize this finding molecularly. The mixture CSMT model is then utilized to predict mixture CMCs, and we find that the predicted CMCs compare very well with the experimental CMCs for various binary mixtures of linear surfactants. This paper lays the foundation for the mixture CSMT framework, which can be used to predict the micellization properties of mixtures of surfactants that possess a complex chemical architecture, and are therefore not amenable to traditional molecular-thermodynamic modeling.