The electron and hole transport perpendicular to the plane of the layers in a-Si:H, F/a-Si, Ge:H, F multilayers is analyzed. We measure the electron dark conductivity σd and its activation energy Ea, d, the photo conductivity σph and its exponent γ, the electron and hole mobility-deep trapping lifetime (μτd)e, h and the hole mobility-recombination lifetime (μτr)h. We identify three regions of barrier thickness ds with very different transport properties: (a) ds≲50Å, dominated by tunnelling between quantum confined states in the bottom of the wells; (b) 50Å ≲ds≲200Å, in which the well acts as the provider of an extra, controllable tail state density; and (c) ds≳200Å, where the individual layers are essentially decoupled.