We apply a recently proposed multiscale simulation approach to study the dynamical properties of polymer blend interfaces. We use this approach to study the influence of the bulk rheological properties of the polymer blend components upon the slip at unentangled polymer interfaces. Our numerical results agree quite well with the predictions from scaling approaches and phenomenological theories. Moreover, these results also provide a microscopic explanation of the negatively deviating viscosities of polymer blends. We also present results elucidating the slip suppressing influence of block copolymer compatibilizers. Our results suggest that even trace fractions of compatibilizers can suppress slip at polymer interfaces. We study the influences of the molecular weight of the block copolymer and the coverage of block copolymers upon the dynamical properties of polymer blend interfaces, and we suggest some effects that might account for the effect of compatibilizers in the suppression of coalescence during polymer blending.