Soluble surfactants form thick adsorption layers at the air-liquid interface, but classical adsorption models fail to account for it as they treat the adsorption layer as a mathematical plane (of zero thickness). This simplification has produced several inconsistencies between theoretical predictions and experimental results, especially for the surface potential. Here, we develop a new adsorption model for ionic surfactants at the air-water interface that incorporates the effect of the adsorption layer thickness using a modified Poisson-Boltzmann equation that integrates information from molecular dynamics simulation. We show that the surface potential depends sensitively on both the thickness of the adsorption layer and the interfacial depth at which the surface potential is probed. This model, therefore, provides a much more accurate picture of the surface potential than classical models.