The Monte Carlo (MC) method is widely used to solve various problems in radiotherapy. There has been an impetus to accelerate MC simulation on GPUs whereas thread divergence remains a major issue for MC codes based on acceptance-rejection sampling. Inverse transform sampling has the potential to eliminate thread divergence but it is only implemented for photon transport. Here, we report a MC package Particle Transport in Media (PTM) to demonstrate the implementation of coupled photon-electron transport simulation using inverse transform sampling. Rayleigh scattering, Compton scattering, photo-electric effect and pair production are considered in an analogous manner for photon transport. Electron transport is simulated in a class II condensed history scheme, i.e., catastrophic inelastic scattering and Bremsstrahlung events are simulated explicitly while subthreshold interactions are subject to grouping. A random-hinge electron step correction algorithm and a modified PRESTA boundary crossing algorithm are employed to improve simulation accuracy. Benchmark studies against both EGSnrc simulations and experimental measurements are performed for various beams, phantoms and geometries. Gamma indices of the dose distributions are better than 99.6% for all the tested scenarios under the 2%/2 mm criteria. These results demonstrate the successful implementation of inverse transform sampling in coupled photon-electron transport simulation.