Ion-induced electron emission (IIEE) is an important process whereby ions impinging on a material surface lead to net emission of electrons into the vacuum. While relevant for multiple applications, IIEE is a critical process of electric thruster (ET) operation and testing for space propulsion, and, as such, it must be carefully quantified for safe and reliable ET performance. IIEE is a complex physical phenomenon, which involves a number of ion-material and ion-electron processes, and is a complex function of ion mass, energy, and angle, as well as host material properties, such as mass and electronic structure. In this paper, we develop a discrete model of kinetic IIEE to gain a more accurate picture of the electric thruster chamber and facility material degradation processes. The model is based on three main developments: (i) the use of modern electronic and nuclear stopping databases, (ii) the use of the stopping and range of ions in matter to track all ion and recoil trajectories inside the target material, and (iii) the use of a scattering Monte Carlo approach to track the trajectories of all mobilized electrons from the point of first energy transfer until full thermalization or escape. This represents a substantial advantage in terms of physical accuracy over existing semi-analytical models commonly used to calculate kinetic IIEE. We apply the model to Ar, Kr, and Xe irradiation of W and Fe surfaces and calculate excitation spectra as a function of ion depth, energy, and angle of incidence. We also obtain minimum threshold ion energies for net nonzero yield for each ion species in both Fe and W and calculate full IIEE yields as a function of ion energy and incidence angle. Our results can be used to assess the effect of kinetic electron emission in models of full ET facility testing and operation.