We consider a planar, cylindrical, or spherical particle immersed in an arbitrary a:b electrolyte solution. The particle comprises an ion-impenetrable, rigid uncharged core and an ion-penetrable membrane carrying nonuniformly distributed fixed charges. This model simulates a wide class of biocolloids and particles covered with an artificial surface layer. Two classes of nonuniform fixed charge distributions, one linear and the other nonlinear, are examined. These distributions all have the same average or apparent space charge density, which is independent of the geometry of the particle. On the basis of a perturbation method, the distribution of the gradient of the electrical potential of the system under consideration is derived, and the essential thermodynamic properties of the electrical double layer are estimated. The result of numerical simulation reveals that the degree of accuracy of the present semi-analytical treatment is satisfactory. We show that the distribution of fixed charges in membrane phase has a significant effect on the thermodynamic properties of the system under consideration. Assuming that the fixed charges are distributed homogeneously may lead to an appreciable deviation.