Aims. We inverted a spectropolarimetric scan of an active region and a filament (240 × 340 arcsec) achieved with THEMIS on 7 December 2003 in the two lines Fe i 6302.5 and 6301.5 Å.Methods. The inversion was achieved for each line separately by using the UNNOFIT code of Landolfi and Landi Degl'Innocenti, and was improved by introducing a magnetic filling-factor parameter. The magnetic and non-magnetic theoretical atmospheres, mixed in the proportion given by the filling factor, were derived from the same set of parameters, except for the presence (or absence) of a magnetic field. The fundamental ambiguity is not solved. Results. The tests run with UNNOFIT show that the magnetic field strength B and the magnetic filling factor α cannot be separately recovered by the inversion in Fe i 6302.5, but that their product αB, which is the local average magnetic field, is recovered. The magnetic flux is only its longitudinal component. In addition, the results make two regimes clearly appear, corresponding to two ranges of local average magnetic field strength as measured in 6302.5: (a) the network, having a field inclined of about 20• -30• from the vertical in 6302.5 (spread more but non-horizontal in 6301.5), with a homogeneous azimuth. In this zone the local average field strength in 6302.5 is higher than 45 Gauss; (b) the internetwork, where the field is turbulent (with a horizontal trend, spread more at lower altitudes), and the 6302.5 local average field strength is lower than 45 Gauss (about 20 Gauss). Conclusions. The two lines display coherent results, in particular for the magnetic-field azimuth. From this coherence we conclude that the turbulence of the 20 Gauss internetwork field has a solar origin.