The authors derive the distribution of the phase difference between two multilook scattering signals for a multilayer stack with randomly rough surfaces under a plane wave excitation. First, for infinite slightly rough surfaces described by Gaussian centred stochastic processes, the authors show that the underlying complex scattering signals follow a Gaussian joint distribution. Also, it is demonstrated that this property is within the scope of the first-order perturbation theory. Secondly, the authors use this joint probability law to derive the closed-form expression for the probability density function of the phase difference. The theoretical formula is verified by comparison with Monte-Carlo simulations. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.