The electrical behavior of aluminum nitride (AlN) thin film structures consisting of alternating AlN and platinum (Pt) layers has been studied. Typical single layer AlN thin films are insulating due to the wide bandgap properties of the material, but stacked AlN-Pt structures can be conductive. Conductivity studies of the structures indicate regions of semiconductor behavior as well as regions where tunneling occurs. The thickness of the AlN layers, as well as the number of AlN-Pt interfaces in the structures, is found to impact the conduction and tunneling mechanism. Fowler-Nordheim theory and plots were used to determine trends in the electrical behavior and it was found that the field enhancement factor depends on the total thickness of the AlN layers, while the conduction mechanism, tunneling, or multistep hopping between midbandgap states, depends on the number of interfaces as well.