Two AlInN/AlN/GaN heterostructures with 280-nm- and 400-nm-thick AlN buffer grown on sapphire substrates by metal-organic chemical vapor deposition (MOCVD) have been investigated by x-ray diffraction (XRD), atomic force microscopy (AFM), photoluminescence (PL) and Hall-effect measurements. The symmetric (0002) plane with respect to the asymmetric (102) plane in the 280-nm-thick AlN buffer has a higher crystal quality, as opposed to the 400-nm-thick buffer. The thinner buffer improves the crystallinity of both (0002) and (102) planes in the GaN layers, it also provides a sizeable reduction in dislocation density of GaN. Furthermore, the lower buffer thickness leads to a good quality surface with an rms roughness of 0.30 nm and a dark spot density of 4.0 x 10(8) cm(-2). The optical and transport properties of the AlInN/AlN/GaN structure with the relatively thin buffer are compatible with the enhancement in its structural quality, as verified by XRD and AFM results.