We investigate the influence of the Mo-layer thickness on the EUV reflectance of Mo/Si mirrors with a set of unpolished and interface-polished Mo/Si/C multilayer mirrors. The Mo-layer thickness is varied in the range from 1.7 nm to 3.05 nm. We use a novel combination of specular and diffuse intensity measurements to determine the interface roughness throughout the multilayer stack and do not rely on scanning probe measurements at the surface only. The combination of EUV and X-ray reflectivity measurements and near-normal incidence EUV diffuse scattering allows to reconstruct the Mo layer thicknesses and to determine the interface roughness power spectral density. The data analysis is conducted by applying a matrix method for the specular reflection and the distorted-wave Born approximation for diffuse scattering. We introduce the Markov-chain Monte Carlo method into the field in order to determine the respective confidence intervals for all reconstructed parameters. We unambiguously detect a threshold thickness for Mo in both sample sets where the specular reflectance goes through a local minimum correlated with a distinct increase in diffuse scatter. We attribute that to the known appearance of an amorphous-to-crystallization transition at a certain thickness threshold which is altered in our sample system by the polishing.