Radiative recombination from the AlxGa1-xAs-GaAs heterostructure interface was investigated using photoluminescence and photoluminescence-excitation spectroscopy in modulation-doped and undoped samples. This emission is identified as H-band A, resulting from an indirect excitonlike transition in real space. The exciton is made up of a two-dimensional electron in the interface notch and a valence-band hole in the neutral region, having a binding energy of 1.8 meV. The H-band A exciton is directly excited by a free exciton making a vertical transition in real space. H-band A may be a distortion of the vertical direct free exciton in real space to an indirect free exciton in real space, in which case only one exciton is involved; or it could result from the direct excitation of the indirect exciton in real space by the vertical exciton through wave-function overlap, with energy and momentum being conserved. In the latter case two excitons are involved. While the exact coupling mechanism between the free exciton and the H-band A exciton is not well understood, two possibilities are suggested.