A compact quantitative model based on oxide semiconductor interface density of states (DOS) is proposed for Al$_{0.25}$Ga$_{0.75}$N/GaN metal oxide semiconductor high electron mobility transistor (MOSHEMT). Mathematical expressions for surface potential, sheet charge concentration, gate capacitance and threshold voltage have been derived. The gate capacitance behaviour is studied in terms of capacitance–voltage (CV) characteristics. Similarly, the predicted threshold voltage ($V_T$) is analysed by varying barrier thickness and oxide thickness. The positive $V_T$ obtained for a very thin 3 nm AlGaN barrier layer enables the enhancement mode operation of the MOSHEMT. These devices, along with depletion mode devices, are basic constituents of cascode configuration in power electronic circuits. The expressions developed are used in conventional long-channel HEMT drain current equation and evaluated to obtain different DC characteristics. The obtained results are compared withexperimental data taken from literature which show good agreement and hence endorse the proposed model.