Utilizing neutron reflectometry, we have determined the segment density (volume fraction) profiles of the deuteriopolystyrene (dPS) block of a diblock copolymer of poly(styrene-d8-b-2-vinylpyridine) (dPS-PVP) segregating to the interface between the homopolymers PS and PVP as a function of phi(infinity), the volume fraction of diblock copolymer remaining in the host homopolymer after annealing the specimens to reach the equilibrium segregation. These segment density profiles were used to determine the interfacial excess (z*i), which was found to be in good agreement with direct measurements of z*i using forward recoil spectrometry. The interaction parameter chi(PS-PVP) was established from the best fit of a self-consistent mean field (SCMF) theory to the measured segregation isotherm, i.e., z*i versus phi(infinity). With this chi(PS-PVP), the SCMF theory can reproduce the experimental volume fraction profile of the dPS block accurately except very close to the interface; the measured profile is broader at the interface as compared to the predicted profile. This excess broadening is observed for all phi(infinity)'s and tends to be enhanced as z*i increases. We believe that most of the interface broadening is due to the ''roughening'' of the equilibrium interface encouraged by the decrease in interfacial tension accompanying the copolymer segregation. Excellent agreement between the measured profiles and the theoretical predictions of SCMF theory at various phi(infinity)'s is found if a Gaussian convolution is used to represent the effect of the interfacial roughness.