Experiments in the context of block copolymer electrolyte materials have observed intriguing dependence of the ionic conductivities upon the polymer molecular weight and the degree of segregation between the blocks. Such results have been partly rationalized by invoking the spatial extent of dynamical inhomogeneities that manifest in ordered phases of block copolymers comprised of a rubbery and a glassy block. Motivated by such observations, we use molecular dynamics simulations to study the extent of spatial inhomogeneities in segmental dynamics of lamellar diblock copolymer systems where the blocks possess different mobilities. We probed the local average relaxation times and the dynamical heterogeneities as a function of distance from the interface. Our results suggest that the relaxation times of rubbery segments are strongly influenced by both the spatial proximity to the interface and the relative mobility of the glassy segments. Scaling of our results indicate that the interfacial width of the ordered phases serves as the length scale underlying the spatial inhomogeneities in segmental dynamics of the fast monomers. (C) 2016 Wiley Periodicals, Inc.