We study the properties of electrical double layers separated by a charged plate of finite thickness. The nonlinear Poisson-Boltzmann equation is analytically solved for this system. It is shown that, for an unsymmetrically charged, narrow plate, the charged fluids at both sides of the plate are strongly correlated, and the local electroneutrality condition (LEC) is not satisfied. The LEC is satisfied only for an infinitely thick plate. Analytical expressions for the induced charge and mean electrostatic potential are given and analyzed. These findings could be relevant for the understanding of protein adsorption on membranes.