Angle-resolved photoemission spectroscopy (ARPES) is a powerful technique for the study of electronic structure, but it lacks a direct ability to study buried interfaces between two materials. We address this limitation by combining ARPES with soft X-ray standing-wave (SW) excitation (SWARPES), in which the SW profile is scanned through the depth of the sample. We have studied the buried interface in a prototypical magnetic tunnel junction La0.7Sr0.3MnO3/SrTiO3. Depth-and momentum-resolved maps of Mn 3d eg and t2g states from the central, bulk-like and interface-like regions of La0.7Sr0.3MnO3 exhibit distinctly different behavior consistent with a change in the Mn bonding at the interface. We compare the experimental results to state-of-the-art density-functional and one-step photoemission theory, with encouraging agreement that suggests wide future applications of this technique.