  Using a recently developed formalism of quantization of radiation in the
presence of absorbing dielectric bodies, the problem of photon tunneling
through absorbing barriers is studied. The multilayer barriers are described in
terms of multistep complex permittivities in the frequency domain which satisfy
the Kramers--Kronig relations. From the resulting input--output relations it is
shown that losses in the layers may considerably change the photon tunneling
times observed in two-photon interference experiments. It is further shown that
for sufficiently large numbers of layers interference fringes are observed that
cannot be related to a single traversal time.
