(N,V,T) Monte Carlo simulations are performed in the framework of the restricted primitive model to monitor the influence of the surface charge distribution on the mechanical stability of charged lamellae neutralized by divalent counterions. The results exhibit a strong influence of the interionic correlations on the ionic structures within the layers of counterions condensed in the vicinity of the charged lamellae. We further analyze the influence of the relative position of the networks of surface sites on the stability of these charged interfaces. This study illustrates how the lateral motion of two charged lamellae contributes to partially relax the longitudinal constraints that occur during the compression of charged interfaces.