The line shape and magnitude of the low-temperature, photon-assisted tunneling current is examined in a nonideal double-quantum-well structure with independent contacts. We include inhomogeneous broadening effects due to processes such as heterointerface roughness or nonuniform doping and scattering by the short-range potential. We show that the interplay between the inhomogeneous and homogeneous broadening mechanisms can modify the line shape of the resonant tunnel current between a predominantly Gaussian and a Lorentzian peak shape. Numerical estimates of the linewidths and comparison between amplitudes of the dark and photon-assisted contributions to the tunneling current are presented. We conclude that the integrated total photon-assisted tunneling current is maximized relative to the dark current when the inhomogeneous broadening is minimized, while the peak current value depends both on the homogeneous and inhomogeneous scattering processes.