A binary monolayer adsorbed on a solid surface can separate into distinct phases that further self-assemble into various two-dimensional patterns. The surface stresses in the two phases are different, causing an elastic field in the substrate. The self-organization minimizes the combined free energy of mixing, phase boundary, and elasticity. One can obtain diverse patterns by using substrates with various crystalline symmetries. Consider the pattern of a set of periodic stripes. The stripe orientation depends on the anisotropy in surface stress, substrate stiffness, and phase boundary energy. A more powerful and flexible way is to use a layered substrate. Surface properties designed for the applications of those patterns can be obtained by choosing appropriate materials and structures for the monolayer and the top layer of the substrate. The subsequent layers of the substrate provide the required stiffness anisotropy, the effect of which is passed to the monolayer patterns through the elastic field. We solve the elastic field in the anisotropic, heterogeneous, three-dimensional half-space by using the Eshelby–Stroh–Lekhnitskii formalism and the Fourier transformation. Depending on the thicknesses and the degrees of the stiffness anisotropy of the substrate layers, the lowest energy stripes can have tunable equilibrium size and orientation. We also discuss other possibilities of manipulating the phase patterns by engineering the elastic field.