In this paper, the authors present a polarisation dependent analytical model for DC, radio frequency (RF) and linearity characteristics of a proposed lattice-matched AlInN/AlN/GaN metal-oxide-semiconductor high electron mobility transistor (MOSHEMT). The developed model includes charge controlled analysis derived from triangular potential well approximation along with the spontaneous and piezoelectric polarisation effects. The model accurately predicts the threshold voltage, two-dimensional electron gas sheet charge density, drain current, transconductance and cut-off frequencies for different samples of gate dielectric materials such as SiO2, HfO2 and Al2O3 over a full range of gate and drain bias. A detailed analysis of the linearity characteristics by investigating the key figure-of-merit metrics such as second-order voltage intercept point, third-order voltage intercept point, third-order input intercept point and third-order intermodulation distortion are performed for different gate dielectric thicknesses of 5, 7 and 10 nm. The accuracy of the model results is verified against Silvaco Technology Computer Aided Design numerical simulation results and found to be satisfactory. It is observed that by careful tuning the device parameters such as dielectric constant and dielectric thickness, lattice-matched AlInN/AlN/GaN MOSHEMT can considerably improve the device performance and suitable for high performance low distortion RF applications.