Monte Carlo simulations of the interface between the external surface of montmorillonite and aqueous cetylpyridinium chloride (CPCl) solution at ambient conditions are reported and compared with the preceding simulation study of muscovite. Simulation results reveal that a segregation of inorganic ions into the regions near the montmorillonite-water and bilayer-water interfaces leads to a nearly complete displacement of water molecules from the intermediate region of the bilayer aggregate. Such segregation does not occur for muscovite because of a considerably higher surface concentration of inorganic cations compensating its mineral charge. The presence of hydrated inorganic ions in the interfacial region containing the aliphatic part of the bilayer aggregate on muscovite leads to a more compact aggregate structure in agreement with a previously experimentally observed effect of added electrolyte. It also results in a lateral segregation of hydrophilic and hydrophobic clusters in this region in agreement with earlier experimental observations of striped surfactant structures on the muscovite surface. A configuration of the surfactant adsorption complex is found to strongly depend on the water content at the mineral-aggregate interface and suggested to be controlled by the types of inorganic counter- and co-ions present there. A transformation between characteristic configurations of the surfactant adsorption complexes is proposed as an explanation for previous experimental observations of the slow secondary surfactant adsorption.