The morphological stability of the interphase boundaries is a challenging problem, both from mathematical and physical point. In materials that are exposed to thermodynamic potential gradients, $i.e.$, gradients of chemical potentials, electrical potential, temperature, or pressure, transport processes of the mobile components occur. In addition, changes in the morphology of the material surfaces and interfaces may appear. In this paper, a comprehensive formal treatment of the coupled morphological stability of multiple phase boundaries will be given for oxides that are exposed to an oxygen potential gradient. In the Part I of this paper the stability of the diffusionally interacting boundaries of a single oxide layer was explored using the original new method. The exact results obtained by this method where compared to the results obtained by the quasi-stationary approximation, which appeared to be quite precise. In the present communication we study the system of two adjacent oxide layers, i.e. the morphological stability of the three diffusionally interacting boundaries.