The site-binding theory of Yates, Levine, and Healy is extended to include the possibility that counter-ion binding of anions and cations occurs at different distances from the insulator surface. A method for straightforward computation of the ψ0/σ0/pH characteristics is given. This theory is applied to the study of electrolyte/insulator/silicon structures, which makes it possible to measure the ψ0/pH characteristics. Measurements are presented for structures where the insulator is γ-Al2O3 deposited by chemical vapour deposition at 900°C. The influence of counter-ion binding on the ψ0/pH curves is a second-order effect compared to the site-dissociation acid/base reactions, but it is clearly visible. Consideration of the influence of the ionic strength of the electrolyte leads to an estimated anion adsorption equilibrium constant in the range of 0.05 to 0.4 mol−1 dm3 in chloride solutions, although no significant influence of the type of ions present could be observed. Application of the theory to existing measurements of the ψ0/pH and σ0/pH curves of SiO2 surfaces indicates that for this material the cation adsorption equilibrium constant is in the order of 0.1 mol−1 dm3.