Internal photoemission (IPE) measurements of the conduction band discontinuities at GaAs/amorphous-Ge interfaces have been carried out at the Vanderbilt Free-Electron Laser (FEL). IPE is a simple and direct measurement capable of unprecedented accuracy. The FEL is uniquely equipped for semiconductor spectroscopy due to its brightness, tunability, and spectral range, 1-8 mum (0.15-1.2 eV). IPE uses FEL photons of sufficient energy to optically pump electrons over the conduction band discontinuity, producing a photocurrent. No complex modeling is required to extract the discontinuity from the experimental data, since it coincides with photocurrent threshold energy. Both linear and Fowler curve fits of the threshold region agree within an accuracy of +/-5 meV. The IPE measurements are in agreement with previous conventional vacuum photoemission measurements that were limited to +/-100 meV accuracy. Unlike conventional vacuum photoemission, IPE does not have the requirement that interfaces must be grown and measured in situ. Since FEL-IPE utilizes subband pp photons, it can be applied to buried interfaces, as well as interfaces under bias. Because of its accuracy and simplicity, systematic use of this technique over a broad range of semiconductor interfaces promises to resolve long-standing disagreements between competing semiconductor band-lineup theories.