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Predicting the non-Newtonian shear response of soft interfaces in biophysical systems and engineered products has been compromised by the use of linear (Newtonian) constitutive equations. We present a generalized constitutive equation, with tractable material properties, governing the response of Newtonian and non-Newtonian interfaces subjected to a wide range of steady shear. With experiments spanning six decades of shear rate, we capture and unify divergent reports of shear-thinning behavior of monomolecular films of the lipid dipalmitoylphosphatidylcholine, the primary constituent of mammalian cell walls and lung surfactant, at near-physiological packing densities.