Diffuse scattering of X rays is a particularly useful tool for studying interface and surface defects in single layer films. We have extended this technique to the study of multilayers. The samples are Mn/Ir(111) superlattices where Mn is pseudomorphic to Ir. We have studied three typical samples prepared at different substrate temperatures. Using theoretical analyses and simulations of both specular and off-specular X-ray scattering data at small angles as well as large angles, we show that large length-scale interfacial roughness is mainly due to the formation of terraces during growth at low deposition temperature, whereas small length-scale interfacial roughness occurs preferably at high deposition temperature and is mainly due to an atomic interdiffusion (i.e. the formation of an interface alloy) which manages to maintain a high degree of crystallographic order.