A planar interface between immiscible phases in a symmetric polymer blend is studied in self-consistent field theory for completely flexible (Gaussian) and semiflexible (wormlike) chains. Concentration and density profiles, chain end distributions, interfacial tensions, and the orientational order of whole chains and single monomers are calculated. The results are compared with data from Monte Carlo simulations. The qualitative agreement is overall very good. Quantitatively, the theory succeeds in predicting the correct profile widths only in the limit of extremely long chain lengths, and only for small values of the Flory-Huggins parameter chi.