In this paper we develop a theoretical model describing water motion in a coupled borehole-subglacial flow system. The theory applies to basal drainage systems having multiple and extensive interconnected flow paths. Within this domain it encompasses a broad range of flow regimes, from laminar Darcian flow in a thick permeable unit to turbulent sheet flow in a very thin layer. Important terms in the model are highlighted by recasting the problem in dimensionless form. The non-dimensional formulation indicates that there are four free parameters in the coupled system. These parameters characterize skin friction in the borehole, and diffusion, transmissivity and turbulent transport in the subglacial flow layer. Dimensionless results show that, under most circumstances, the effects of skin friction in the borehole are negligible. Diffusion, transmissivity and especially turbulent transport in the basal layer are found to influence subglacial water flow strongly. We use our model to predict fluctuations of borehole-water levels that result from different types of disturbances. We show how this framework can be used to estimate subglacial hydraulic properties by comparing model results with data collected during field experiments on Trapridge Glacier, Yukon Territory, Canada in 1989 and 1990.