A self-consistent-field theory for compressible polymer mixtures is developed by introducing elements of classical density functional theory into the framework of the Helfand theory. It is then applied to study free surfaces of binary (A,B) polymer blends. Density profiles in the one- and two-phase region are calculated as well as chain end distributions and chain orientations of the minority and the majority component. In the ideally symmetric mixture, in which the individual properties of polymers A and B are the same and both have the same surface energy, polymers of the minority component segregate to the surface, where they are exposed to less polymers of the majority component. This effect can only be captured correctly, if one accounts for the fact that the monomer-monomer interaction has finite range. As a consequence, the Flory-Huggins-parameter varies in space and depends on the concentration profiles and their derivatives. The surface segregation calculated with such an ansatz, without any fit parameter, is in reasonable quantitative agreement with data from recent Monte Carlo simulations.