The role of the basement membrane is vital in maintaining the integrity and structure of an epithelial layer, acting as both a mechanical support and forming the physical interface between epithelial cells and the surrounding connective tissue. The function of this membrane is explored here in the context of a growing epithelial monolayer, defined such that the epithelial cells divide and migrate along a deformable substrate. A discrete, off-lattice cell-centre modelling approach is undertaken, which permits definition of a basement membrane component, separating the epithelial cells from the tissue stroma whilst responding to forces from both that arise due to cell division, migration and apoptosis. This model is applicable to a range of biological epithelia, including the self-renewing interfollicular epidermis, the olfactory epithelium and the intestinal crypts of Lieberkühn, to inform response and recovery of such tissues following injury. Model simulations show that homeostasis of the growing monolayer can be achieved and sustained, and the necessary balance of interactive cell forces, cell migration and cell death is presented. This work is proposed as a novel extension to the body of discrete models of biological epithelia, permitting investigation of the growth and migration of epithelial cells in a deformable environment.