<p>Within the framework of the linearized theory of stability of deformable bodies, a plane problem on compression of a semi-bounded piecewise-homogeneous body with a coating layer (bilayer) along a frictionless sliding zone located at the rectilinear interface is considered. A semi-analytical approach was used, previously tested by the authors in the case when the roots of the characteristic equations for the elastic potentials of both materials of the body being equal. In this work, the resolving homogeneous Fredholm integral equation of the first kind is obtained in a general form for a combination of two different materials with an arbitrary structure of their elastic potential. All four possible cases of relationships between the roots of the characteristic equations for such materials are considered. From the solution of eigenvalue problems, critical values of the compressive load parameters corresponding to a local loss of stability of the material near the sliding zone were determined, and the nature of their dependence on the relative coating thickness and on the mechanical characteristics of the body was studied for a number of specific pairs of elastic potentials that describe the components of a piecewise-homogeneous body. The influence of the structure of elastic potentials on the critical values of the load parameters was also investigated, and a comparison of the results with the results of the problem on compression of a similar body along an interface crack was carried out.</p>