The exceptional strength of nanolaminates is attributed to the influence of their fine stratification on the movement of dislocations. Through atomistic simulations, the impact of interfacial structure on the dynamics of an edge dislocation, which is compelled to move within a nanoscale layer of a nanolaminate, is examined for three different nanolaminates. In this study, we model confined layer slip in three structures: nanolaminated Ag and two types of Ag/Cu nanolaminates. We find that the glide motion is jerky in the presence of incoherent interfaces characterized by distinct arrays of misfit dislocations. In addition, the glide planes exhibit varying levels of resistance to dislocation motion, where planes with intersection lines that coincide with misfit dislocation lines experience greater resistance than planes without such intersection lines.