It is well accepted that unabsorbed as well as absorbed AGN are needed to explain the nature and the shape of the Cosmic X-ray background, even if the fraction of highly absorbed objects (dubbed Compton-thick sources) substantially still escapes detection. We derive and analyze the absorption distribution using a complete sample of AGN detected by SwiftBAT in the first three years of the survey. The fraction of Compton-thick AGN represents only 4.6% of the total AGN population detected by SwiftBAT. However, we show that once corrected for the bias against the detection of very absorbed sources the real intrinsic fraction of Compton-thick AGN is 20 9 −6%. We proved for the first time (also in the BAT band) that the anti-correlation of the fraction of absorbed AGN and luminosity it tightly connected to the different behavior of the luminosity functions (XLFs) of absorbed and unabsorbed AGN. This points towards a difference between the two subsamples of objects with absorbed AGN being, on average,intrinsically less luminous than unobscured ones. Moreover the XLFs show that the fraction of obscured AGN might also decrease at very low luminosity. This can be successfully interpreted in the framework of a disk cloud outflow scenario as the disappearance of the obscuring region below a critical luminosity. Our results are discussed in the framework of population synthesis models and the origin of the Cosmic X-ray Background. Show Partial Abstract