A high performance triple-heterojunction (3HJ) design has been previously proposed for tunneling FETs (TFETs). Compared with single HJ TFETs, the 3HJ TFETs have both shorter tunneling distance and two transmission resonances that significantly improve the ON-state current (I _ON ). Coherent quantum transport simulation predicts that I _ON = 460 μA/μm can be achieved at gate length Lg = 15 nm, supply voltage V _DD = 0.3 V, and OFF-state current I _OFF = 1 nA/μm. However, strong electron-phonon and electron-electron scattering in the heavily doped leads implies that the 3HJ devices operate far from the ideal coherent limit. In this paper, such scattering effects are assessed by a newly developed multiscale transport model, which combines the ballistic nonequilibrium Green's function method for the channel and the drift-diffusion scattering method for the leads. Simulation results show that the thermalizing scattering in the leads both degrades the 3HJ TFET's subthreshold swing through scattering-induced leakage and reduces the turn-ON current through the access resistance. Assuming bulk scattering rates and carrier mobilities, the I _ON is dropped from 460 μA/μm down to 254 μA/μm, which is still much larger than the single HJ TFET case.