We investigated the influence of the thickness of the AlN interlayer for InAlN/GaN and InAlN/AlGaN/GaN heterostructures. The AlN thickness strongly affects the surface morphology and electron mobility of the InAlN/GaN structures. The rms roughness of the surface increases from 0.35 to 1.2nm with increasing AlN thickness from 0 to 1.5nm. Large pits are generated when the AlN is thicker than 1nm. The highest electron mobility of 1470cm²/V·s is obtained for a 0.75-nm-thick AlN interlayer. The mobility, however, becomes lower with increasing deviation from 0.75nm. It is only 200cm²/V·s for the 0-nm thick AlN. Inserting AlGaN between AlN and InAlN suppresses the influence of the AlN interlayer thickness. A smooth surface with rms roughness of 0.35nm is obtained for all samples with 0-1.5-nm-thick AlN. The electron mobility ranges from 1000 to 1690cm²/V·s. The variation is smaller than that for InAlN/GaN. We fabricated field effect transistors (FETs) with gate length of 2µm. The electron mobility in the access region affects the transconductance (g_m) of FETs. As a results, the influence of the AlN thickness for InAlN/GaN FETs is larger than that for InAlN/AlGaN/GaN FETs, which reduces gate leakage current. The transconductance varies from 93 to 235mS/mm for InAlN/GaN FETs. In contrast, it varies from 180 to 230mS/mm for InAlN/AlGaN/GaN FETs. These results indicate that the InAlN/AlGaN/GaN heterostructures could lead to the development of GaN-based FETs.