The interaction energy between two plates covered with charge-regulation layers is calculated based on a linearized Poisson-Boltzmann equation. By a comparison with the exact solution, the accuracy of the approximate solutions obtained by linear superposition approximation and the regular perturbation method can be examined. The range of the validity for both approximations is therefore determined. These results may shed some light on the interaction between two spheres, which is complicated and often investigated by the approximate approaches.