This article presents a novel mixed-thermoelastohydrodynamic (TEHD) model for the lateral lubricating interfaces which exist between floating lateral bushings and gears in external gear machines (EGMs). The proposed model integrates the influence of surface asperities along with the fluid structure and thermal interaction in the interface, especially in the regions of very low film thicknesses by following a stochastic approach in modelling the mixed lubrication regime. Furthermore, the current work includes validation of the predictions of the mixed-TEHD model against experimentally measured leakages from the lateral gap and compares the performance of this model with a previously developed full film TEHD model for the lateral gaps in EGMs.