A lattice model is proposed to explain the restructuring of an ionic surfactant absorbed on a charged surface. When immersed in water, an ionic mica plate initially covered by a monolayer of surfactants rearranges to a surface inhomogeneously covered by patches of surfactant bilayer and bare mica. The model considers four species that can cover lattice sites of a surface. These species include (i) a surfactant molecule with its headgroup down, (ii) surfactant molecule with the headgroup up, (iii) a surfactant dimer arranged in a tail-to-tail configuration, which is a part of a bilayer, and (iv) a mica lattice site covered by water. We consider that only nearest neighbors on the lattice interact and describe the interactions by an interaction matrix. Using this model, we perform Monte Carlo simulations and study how the structure of the inhomogeneous surface depends on the interaction between water covered lattice site and its neighboring surfactant species covered sites. We observe that when this interaction is absent, the system undergoes phase separation into a bilayer phase and mica surface covered with water. When this interaction is taken into account, patches of surfactant bilayer and water are present in our system. The interaction between mica surfaces covered by patches of ionic surfactants is studied in experiments to understand the nature of long-ranged "hydrophobic" forces.