Full-waveform inversion (FWI), as an optimization-based approach to estimating subsurface models, is limited by incomplete acquisition and illumination of the subsurface. The incorporation of additional data from new and independent ray paths should be expected to result in significant increase in the accuracy of FWI models. In principle, seismic-while-drilling (SWD) technology can supply these additional ray paths; however, it introduces a new suite of unknowns, namely precise source locations (i.e., drilling path), source signature, and radiation characteristics. Here we formulate a new FWI algorithm in which source radiation patterns and positions join the velocity and density values of the grid cells as unknowns to be determined. We then conduct several numerical inversion experiments with different source settings, using a synthetic model. The SWD sources are supplemented by explosive sources and multi-component receivers at the surface, simulating a conventional surface acquisition geometry. The subsurface model and SWD source properties are recovered and analyzed. The analysis is suggestive that SWD involvement can enhance the accuracy of FWI models, with varying degrees of enhancement depending on factors such as trajectory inclination, source density, and drill path extension. The impact of SWD-FWI over standard FWI is reduced when low-frequency data are missing, but improvements over the models constructed with no subsurface sources remain. This formulation permits general source information, such as position and moment tensor components, to be independently obtained. This inversion scheme may lead to a range of potential applications#xD;where both medium properties and source information are required.