  We derive a theory for transmission through disordered finite superlattices
in which the interface roughness scattering is treated by disorder averaging.
This procedure permits efficient calculation of the transmission thr ough
samples with large cross-sections. These calculations can be performed
utilizing either the Keldysh or the Landauer-B\"uttiker transmission
formalisms, both of which yield identical equations. For energies close to the
lowest miniband, we demonstrate the accuracy of the computationally efficient
Wannier-function approximation. Our calculations indicate that the transmission
is strongly affected by interface roughness and that information about scale
and size of the imperfections can be obtained from transmission data.
