The effective far-infrared response of a superconductor-normal metal (S/N) composite is studied within the effective medium approximation. In particular, the effects of a finite relaxation time tau-S, which represents a generalization of the tau-S = 0 Mattis-Bardeen form, are studied. The effects of varying tau-S and the concentration of the superconducting component on the effective conductivity and effective reflectivity of the composite are investigated. Possible applications of our calculations to the high temperature superconductors are discussed.