We present an analytical theory for the competing influences of polymer-surface and polymer-polymer interactions, density and composition variations, and blend asymmetries on the surface profiles of a multicomponent polymer blend near an interacting, impenetrable interface. The theory is explicitly applied in the limit of small continuum model polymer-surface interaction parameters, a limit which still enables treating all qualitative behaviors of polymers that individually tend either to aggregate toward or to segregate from the surface. The formulation is based on an analytic combined self-consistent field-density functional theory for inhomogeneous polymer systems. The theory describes the compressible polymer system with a generic Gaussian chain-random mixing type model, which in the bulk phase reproduces a Sanchez-Lacomb-type description of the bulk thermodynamics. The analytic expressions for the density profiles, surface excesses, surface densities? and surface correlation lengths are all presented explicitly for binary compressible systems, but we note how to make the trivial extension to more components. The surface excess and surface correlation length are shown to diverge along the bulk phase spinodal, in rough accord with the increases found in recent experiments by Genzer and Composto. The relation between the continuum model interaction parameters and microscopic (e.g., lattice-model-type) interaction parameters is used to understand recent observations of a surface free energy that displays a higher than quadratic dependence on the surface composition and of the strong surface segregation exhibited by isotopic polymer blends.