The forward current-voltage (I-V) characteristics of Ni/Au Schottky contacts on AlGaN/GaN heterostructures have been studied in this work. The electrical characteristics exhibited a strongly non-ideal behavior that could not be described by the thermionic emission theory. Hence, we used a "two diodes model," considering both the presence of the Ni/AlGaN barrier and of a second barrier height at the AlGaN/GaN heterojunction. Capacitance-voltage (C-V) measurements enabled us to experimentally determine the properties of the two dimensional electron gas (2DEG) and, hence, of the second barrier at the AlGaN/GaN interface. Following this approach, the anomalous I-V curves could be explained. Moreover, the value of the barrier height at zero-electric field (flat-band barrier height) was introduced and determined with this procedure, and resulted in a good agreement with literature data based on photoemission measurements. This approach provides a valid procedure for an accurate determination of the barrier height in AlGaN/GaN heterostructures, and the results can have useful implications for the fabrication of AlGaN/GaN HEMTs devices.