The magnetic field vector of the quiet Sun has been first determined by usual Milne-Eddington inversion of ZIMPOL/THEMIS data. But such an inversion provides the local average field only, i.e. the product of the field strength by the magnetic filling factor. To discriminate between both quantities, an additional method has to be provided. We proposed a direct but approached determination of the filling factor in the spectropolarimetric data themselves. Then we were able to derive the inhomogeneous magnetic field strength (i.e. disambiguated from the filling factor). The methods and results from the ZIMPOL/THEMIS data are now published (Bommier et al. 2009). The present paper is intended to show that the THEMIS/THEMIS data, 10 times more numerous, give the same results, validating thus the THEMIS polarimeter results with the ZIMPOL ones. But the main new result is that finally the inhomogeneous field strength is found clearly dependent on the field inclination angle, thus ruling out the hypothesis of a turbulent field. The corresponding field organization could be: thin scattered vertical tubes of strong field opening and weakening with height (in the photosphere). Thus the weak fields would be horizontally (2D) distributed rather than following their generally admitted 3D turbulent structure. This distribution is not incompatible with the Hanle effect observations, because the Hanle effect is insensitive to the vertical field. The distribution of the thin opening tubes remains to be quantized, but spatial horizontal correlations were observed, which suggests that their size would not be very small with respect to the observation pixel size of 0.2-0.5 arcsec.