We develop a mean-field lattice theory of a compressible Liquid copolymer in the framework of the Scheutjens and Fleer theory of polymer solutions and apply it to study the structure and thermodynamics of the free surface of a symmetric diblock copolymer film. The theory predicts that the difference in the interaction energies between the two constituent components causes the segregation of the block component with the weaker interactions to the free surface. The resulting segment density depth profiles of the individual components are oscillatory owing to the connectivity between the blocks. A detailed study of chain shape and bond orientation characteristics provides a microscopic description of the interfacial structure in the disordered as well. as the microphase separated states. The inclusion of compressibility causes the disordered to lamellar microphase transition to occur at higher temperatures and shorter chain lengths than predicted by incompressible theories using the same interaction parameters. A calculation of the surface tension when the copolymer is disordered in the bulk reveals that there exists an interesting and potentially useful situation where the surface tension of an A-B copolymer is significantly lower than that of each of the homopolymers A and B of the same chain length.