A cilia sublayer model of mucous transport in the lung is developed by considering a two-layer model of the fluid. Both the lower peri-ciliary layer and the upper mucous layer are modelled by Newtonian fluids. Cilia are allowed limited penetration into the more viscous upper layer during the effective stroke, otherwise they are wholly located in the peri-ciliary layer. Predictions of the velocity profile in the peri-ciliary and mucous layers and hence rate of mucous transport are made for specified ciliary beat patterns and viscosity ratios. One of the fundamental problems of mucous transport is the interaction between the cilia and the mucus. As a contribution to this study, an asymptotic expansion is obtained for the force distribution and interface shape on a slender body penetrating the interface.