We present a quantitative study of specular and diffuse (non-specular) x-ray and neutron reflectivity from highly aligned phospholipid membranes deposited on solid substrates. The height-height correlation function could be obtained from the diffuse scattering without further model assumptions. The results differ significantly from the linear theory of smectic elasticity. We argue that the diffuse scattering is dominated by static liquid-crystalline defects, rather than thermal fluctuations.