The network simulation method is used to calculate the electrostatic potential distribution for suspended spherical particles made of a charged core surrounded by a permeable membrane with adsorbed charges. The structure of the equilibrium diffuse double layers on both sides of the membrane-electrolyte solution interface is analyzed considering an anion adsorption process described by a Langmuir-type isotherm. It is shown that the thickness of the double layer in the membrane strongly depends on the adsorption constant, while it is almost independent of this constant in the electrolyte solution. The evolution of the electric potential on the core as a function of the electrolyte concentration is also analyzed.