A detailed study of the interface formation between polystyrene (PS) and chlorinated polybutadiene (CPB) at 150 degrees C is carried out on bilayer samples by X-ray reflectometry(XRR) and X-ray diffuse scattering (XDS). An equilibrium melt interfacial width sigma(m)(150 degrees C) = 18.8 +/- 0.3 Angstrom is determined by XRR. Lateral fluctuations being averaged over the coherence area in this method, a, must be considered as originating from both homopolymer interdiffusion (sigma(CPB/PS)) and interfacial roughness (sigma(r)): sigma(m)(2) = sigma(CPB/PS)(2) + sigma(r)(2). Interfacial roughness is generally described in the literature to be due to either a residual roughness from sample preparation (hypothesis 1) or capillary fluctuations building up at the interface (hypothesis 2). The nature and importance of the interfacial roughness are assessed by XDS scans, which include the detection of the diffuse (off-specular) scattering arising from lateral correlations in the roughness profile. While hypothesis 1 can be unambiguously rejected from the analysis of our XDS data, at least two equally valuable fits of theory to data are found under the hypothesis that the interfacial roughness changes during annealing. In the first one, interdiffusion is restricted, and the interfacial width is dominated by roughness (sigma(r) > sigma(CPB/PS)). In the second one, the reverse is true: sigma(CPB/PS) much greater than sigma(r). The former picture is closer to predictions from existing molecular theories of capillarity and gives for the Flory-Huggins interaction parameter computed through mean-field arguments a better agreement with the interaction parameter obtained from solubility parameters of CPB and PS.