MonteCarlo simulations of the interface between the cleaved surface of muscovite mica and aqueous cetylpyridinium chloride (CPCl) solution at ambient conditions are reported. Simulation result reveal that monolayer or bilayer aggregates of CP+ ions at the muscovite-water interface remain incomplete up to a CP+ coverage compensating the negative charge of muscovite. It is predicted that at this CP+ coverage only a partial desorption of K+ ions occurs and the two aggregates can be distinguished with help of the X-ray reflectivity technique. Fort-nation of inner-sphere and outer-sphere adsorption complexes of CP+ ions at distances of similar to 3 angstrom and similar to 5 angstrom, respectively, from the surface is observed. Despite an increasing adsorption of CP+ ions, the structure of the adsorbed water film is largely preserved within similar to 5 angstrom from the surface. A strong decrease of water density beyond this distance and formation of "adsorbed K+"-Cl- ion pairs result in coadsorption of Cl-in an amount equivalent to 1/4 of the negative charge of muscovite as close as similar to 4.3-4.8 angstrom to the Surface for the incomplete bilayer aggregate. For the incomplete monolayer aggregate, no segregation between K+ and CP+ ions and a displacement of K+ ions into the adsorption sites similar to 1.6 angstrom from the surface are observed.