Accurate modeling of charge transport and both thermal and luminescent radiation is crucial to the understanding and design of radiative thermal energy converters. Charge carrier dynamics in semiconductors are well-described by the Poisson-driftdiffusion equations, and thermal radiation in emitter/absorber structures can be computed using multilayer fluctuational electrodynamics. These two types of energy flows interact through radiation absorption/luminescence and charge carrier generation/recombination. However, past research has typically only assumed limited interaction, with thermal radiation absorption as an input for charge carrier models to predict device performance. To examine this assumption, we develop a fully-coupled iterative model of charge and radiation transport in semiconductor devices, and we use our model to analyze near-field and far-field GaSb thermophotovoltaic and thermoradiative systems. By comparing our results to past methods that do not consider cross-influences between charge and radiation transport, we find that a fully-coupled approach is necessary to accurately model photon recycling and near-field enhancement of external luminescence. Because these effects can substantially alter device performance, our modeling approach can aid in the design of efficient thermophotovoltaic and thermoradiative systems.