In this paper we report on the broadband X-ray properties of a complete sample of 33 absorbed Seyfert galaxies hard X-ray selected with integral. The high quality broadband spectra obtained with both xmm, and integral-IBIS data are well reproduced with an absorbed primary emission with a high energy cutoff and its scattered fraction below 2-3 keV, plus the Compton reflection features. A high energy cut-off is found in 30% of the sample, with an average value below 150 keV. The diagnostic plot NH vs Fobs(2-10 keV)/F(20-100 keV) allowed the isolation of the Compton thick objects, and may represent a useful tool for future hard X-ray observations of newly discovered AGN. We are unable to associate the reflection components with the absorbing gas as a torus, a more complex scenario being necessary. In the Compton thin sources, a fraction (but not all) of the Fe K line needs to be produced in a gas possibly associated with the optical Broad Line Region, responsible also for the absorption. We still need a Compton thick medium (not intercepting the line of sight) likely associated to a torus, which contributes to the Fe line intensity and produces the observed reflection continuum above 10 keV. The so-called Iwasawa-Taniguchi effect can not be confirmed with our data. Finally, the comparison with a sample of unobscured AGN shows that, type 1 and type 2 (once corrected for absorption) Seyfert are characterized by the same nuclear/accretion properties (luminosity, bolometric luminosity, Eddington ratio), supporting the unified view.
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