  Tunneling between two-dimensional electron layers with mutually correlated
disorder potentials is studied theoretically. Due to this correlation, the
diffusive eigenstates in different layers are almost orthogonal to each other.
As a result, a peak in the tunnel I-V characteristics shifts towards small
bias, V. This "protects" the peak against the interaction-induced smearing,
since the relaxation rate near the Fermi level is low. If the correlation in
disorder potentials is complete, the peak position and width are governed by
the spin-orbit coupling in the layers; this coupling lifts the orthogonality of
the eigenstates. Possibility to use inter-layer tunneling for experimental
determination of weak intrinsic spin-orbit splitting of the Fermi surface is
discussed.
