A specific luminescence band originating from a heterointerface (H band) has been observed in the photoluminescence spectrum (at 1.7 K) of a single GaAs/GaAlAs heterostructure. Threshold effect of epitaxial temperature on interface luminescence has been found. A model has been proposed which attributes interface luminescence to annihilation of the interface heterodimensional exciton which is composed of a two-dimensional (2D) electron (2D hole) in the notch at the interface and a three-dimensional (3D) hole (3D electron) in the GaAs bulk region near the interface. The exciton binding energy decreases when the interface ruggedness increases. In the case of large inhomogeneities (ruggedness of chemically abrupt interface) such an exciton cannot form and the corresponding H band is not observed in the spectrum. Thus, the luminescence of the interface heterodimensional exciton can serve as an indication of the interface ruggedness.