Using molecular dynamics, we consider the thermal resistances of superlattices consisting of varying numbers of distinct nanolayers of two different materials. These are placed between two water reservoirs at uniform hot and cold temperatures. The interfacial resistances produced between different solid layers can lead to significantly lower heat transfer for a specified temperature difference. Such a large reduction in thermal transport cannot be explained by the interfacial resistance alone. In addition to the interfacial resistance between two adjacent superlattice layers, the relatively wide thermal boundary layers that are produced adjacent to the interfaces introduces a supplementary resistance.