The problem of finding the specific surface energy and work functions of electrons and positrons in a metal with a dielectric coating is solved analytically within the Ritz method and the quantum-statistical functional in the stable jelly model. The calculated values are sensitive to the gradient series of the kinetic energy of noninteracting electrons and are insensitive to the form of the monotonic electron profile. A comparison is made with calculations by the Kohn–Sham method of the surface energy and work functions for specific insulators. The simplest composite coatings are considered. The relationship between the theory of the Ritz method for composite coatings and calculations by the Kohn–Sham method of the surface energy and work function of electrons for metal–dielectric nanosandwiches is analytically established. It is proposed to take into account the effect of the composite coating on the characteristics of the metal surface by scaling the case of a homogeneous coating. The possibility of using the results obtained in various experimental situations is discussed.