We present a structural study of biomimetic lipid bilayers interacting with the antimicrobial peptide magainin 2 amide, using grazing incidence X-ray diffraction and reciprocal space mapping (RSM) techniques. The short-range order of lipid chains in lecithin is found to be strongly reduced by the peptides. From the scattering intensity of the chain correlation peak, we can quantify the lateral length scale R over which the bilayer structure is affected by peptide binding. The non-local perturbation of the bilayer is discussed in the framework of bilayer elasticity theory.