Angular momentum transport in protostellar discs can take place either radially, through turbulence induced by the magnetorotational instability (MRI), or vertically, through the torque exerted by a large-scale magnetic field that threads the disc. Using semi-analytic and numerical results, we construct a model of steady-state discs that includes vertical transport by a centrifugally driven wind as well as MRI-induced turbulence. We present approximate criteria for the occurrence of either one of these mechanisms in an ambipolar diffusion-dominated disc. We derive 'strong field' solutions in which the angular momentum transport is purely vertical and 'weak field' solutions that are the stratified-disc analogues of the previously studied MRI channel modes; the latter are transformed into accretion solutions with predominantly radial angular momentum transport when we implement a turbulent-stress prescription based on published results of numerical simulations. We also analyse 'intermediate field strength' solutions in which both modes of transport operate at the same radial location; we conclude, however, that significant spatial overlap of these two mechanisms is unlikely to occur in practice. To further advance this study, we have developed a general scheme that incorporates also the Hall and Ohm conductivity regimes in discs with a realistic ionization structure.