Semiempirical equilibrium models of competitive, two-component binding of simple ions to heterogeneous materials are based on a combination of independent binding isotherms, such as two-component Langmuir isotherms or exchange isotherms. Such models are usually sufficiently flexible to rationalize various experimental data sets quantitatively. Since such models are thermodynamically consistent, they have substantial predictive capabilities. Furthermore, such models are rather simple, may depend on a relatively small number of parameters, and provide an intuitive framework for comparison of binding properties of different materials. We solve the ill-posed data inversion problem with constrained, regularized least-squares techniques. This approach to the interpretation of two-component competitive ion binding to heterogeneous materials is illustrated with two data sets; the binding of Sr2+ and H+ to ferrihydrite (amorphous FeOOH) and that of Cu2+ and H+ to a humic acid.