Overlapping bulk and two-dimensional excitons have been observed in modulation-doped heterostructures. Their differing behavior in a magnetic field allows them to be studied separately. Both free and bound excitons, associated with the two-dimensional electron gas, have been observed in the photoluminescence spectra of these structures. These excitons show a reduced binding energy due to screening and are found in a region of the structure where band-gap renormalization occurs due to many-body interactions. The two-dimensional excitons are identified from measurements conducted in applied magnetic fields.