Using X-ray scattering, the structure of compressed phospholipid monolayers at the air-water interface matrixed with varying amounts of polymer lipid has been determined. The out-of-plane structure of the monolayer was greatly perturbed by the incorporation of the bulky polymer lipid resulting in a systematic roughening of the interface and a decrease in the coherently Bragg-scattering lipid tail region. Our results indicate that the increased lateral packing stresses due to the hydrophilic polymer chains are predominately relaxed through an increase in lipid protrusions rather than an increased area per lipid molecule.