  Aims. We present a 0.2--200 keV broad-band study of absorbed AGN observed
with INTEGRAL, XMM-Newton, Chandra and ASCA to investigate the continuum shape
and the absorbing/reflecting medium properties. Methods. The sources are
selected in the INTEGRAL AGN sample to have a 20--100 keV flux below
8$\times10^{-11}$ $\flux$ (5 mCrab), and are characterized by a 2--10 keV flux
in the range (0.8--10)$\times10^{-11}$ $\flux$. The good statistics allow us a
detailed study of the intrinsic and reflected continuum components. In
particular, the analysis performed on the combined broad-band spectra allow us
to investigate the presence of Compton reflection features and high energy
cut-off in these objects. Results. The column density of the absorbing gas
establishes the Compton thin nature for three sources in which a measure of the
absorption was still missing. The Compton thin nature of all the sources in
this small sample is also confirmed by the diagnostic ratios F$x/F[OIII]. The
Compton reflection components we measure, reflection continuum and iron line,
are not immediately compatible with a scenario in which the absorbing and
reflecting media are one and the same, i.e. the obscuring torus. A possible
solution is that the absorption is more effective than reflection, e.g. under
the hypothesis that the absorbing/reflecting medium is not uniform, like a
clumpy torus, or that the source is observed through a torus with a very
shallow opening angle. The high energy cut-off (a lower limit in two cases) is
found in all sources of our sample and the range of values is in good agreement
with that found in type 1 Seyfert galaxies. At lower energies there is clear
evidence of a soft component (reproduced with a thermal and/or scattering
model), in six objects.
