The lattice-based self-consistent field theory approach of Scheutjens-Fleer is used to formulate theoretical relationships for description of interfacial thermodynamic properties of multi-component, compressible polymer mixtures adsorbed at a solid surface. A generalized expression for the chemical potential of a polymer chain in a multi-component compressible mixture is derived. A closed-form expression for the interfacial energy in terms of the segment densities and mole-fractions is obtained for a m-component adsorbed mixture.This expression exactly reduces to the Scheutjens-Fleer formalism result in the homopolymer-solvent case and accounts for thermal interactions, unlike previous works [see Ginzburg et al., Macromolecules, 42, 9090 (2009)]. Explicit self-consistent equations and relations for the chemical potential of ternary blends are derived. Equations are also derived for modeling compressible systems via hole-components. Also, using simple mixing rules, the self-consistent equations and chemical potential for compressible binary blends are presented. © 2018, © 2018 Taylor & Francis Group, LLC.