The current transport properties of an n ‐doped, lattice matched AlInN layer with multiple, periodic GaN insertions are reported. Samples with three and seven insertions were grown and mesa structures were etched through the AlInN structures to different depths to determine the voltage contribution from each heterointerface. The quality of the AlInN surface improved with the GaN insertions and with reducing the thickness of the individual AlInN layers from 80 nm to 55 nm. Simulations suggest that the large conduction band discontinuity can lead to high turn on voltages which can be reduced by high levels of doping. Current‐voltage measurements through the full structure show a diode characteristic which is temperature activated. A quasi‐linear current‐voltage characteristic is measured when the current is driven only through the uppermost GaN interlayer with 80 nm thick AlInN layers, indicating current leakage through defects in these layers (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)