The addition of large hydrophobic cations to lead halide perovskites has significantly enhanced the environmental stability of photovoltaic cells based on these materials. However, the associated formation of two-dimensional structures inside the material can lead to dielectric confinement, higher exciton binding energies, wider bandgaps and limited charge-carrier mobilities. Here we show that such effects are not detrimental to the charge transport for carefully processed films comprising a self-assembled thin layer of quasi-two-dimensional (2D) perovskite interfaced with a 3D MAPbI3 perovskite layer. We apply a combination of time-resolved photoluminescence and photoconductivity spectroscopy to reveal the charge-carrier recombination and transport through the film profile, when either the quasi-2D or the 3D layers are selectively excited. Through modeling of the recorded dynamics, we demonstrate that while the charge-carrier mobility is lower within the quasi-2D region, charge-carrier diffusion to the 3D phase leads to a rapid recovery in photoconductivity even when the quasi-2D region is initially photoexcited. In addition, the blue-shifted emission originating from quasi-2D regions overlaps significantly with the absorption spectrum of the 3D perovskite, allowing for highly effective “heterogeneous photon recycling”. We show that this combination fully compensates for the adverse effects of electronic confinement, yielding quasi-2D perovskites with highly efficient charge transporting properties.