Transmission spectra of ordered and disordered GaAs/Al0.3Ga0.7As superlattices (SL) were measured at 2 K. The experimental results are compared with numerical simulations obtained by means of a transfer matrix method. The numerical results indicate that a multiple-quantum-well model accounts for the main features of random SL, and that a disorder-induced fine structure is present. The agreement between the measured spectra and the numerical calculations supports the predicted features.