Amorphous/crystalline nanolaminate composites have aroused extensive research interest because of their high strength and good plasticity. In this paper, the nanoindentation behavior of Cu64Zr36/Cu amorphous/crystalline nanolaminates (ACNLs) is investigated by molecular dynamics (MD) simulation while giving special attention to the plastic processes occurring at the interface. The load–displacement curves of ACNLs reveal small fluctuations associated with shear transformation zone (STZ) activation in the amorphous layer, whereas larger fluctuations associated with dislocations emission occur in the crystalline layer. During loading, local STZ activation occurs and the number of STZs increases as the indentation depth in the amorphous layer increases. These STZs are mostly located around the indenter, which correlates to the high stresses concentrated around the indenter. When the indenter penetrates the crystalline layer, dislocations emit from the interface of amorphous/crystalline, and their number increases with increasing indentation depth. During unloading, the overall number of STZs and dislocations decreases, while other new STZs and dislocations become activated. These results are discussed in terms of stress distribution, residual stresses, indentation rate and indenter radius.