  We re-analyse photometric near-infrared data in order to investigate why it
is so hard to get a consensus for the shape and density law of the bulge, as
seen from the literature. To solve the problem we use the Besancon Galaxy Model
to provide a scheme for parameter fitting of the structural characteristics of
the bulge region. The fitting process allows the determination of the global
shape of the bulge main structure.
  We explore various parameters and shape for the bulge/bar structure based on
Ferrer's ellipsoids and fit the shape of the inner disc in the same process.
The results show that the main structure is a quite standard triaxial boxy
bar/bulge with an orientation of about 13 degree with respect to the Sun-centre
direction. But the fit is greatly improved when we add a second structure,
which is a longer and thicker ellipsoid. We emphasize that our first ellipsoid
represent the main boxy bar of the Galaxy, and that the thick bulge could be
either a classical bulge slightly flattened by the effect of the bar potential,
or a inner thick disc counterpart. We show that the double clump seen at
intermediate latitudes can be reproduced by adding a slight flare to the bar.
In order to better characterize the populations, we further simulate several
fields which have been surveyed in spectroscopy and for which metallicity
distribution function (MDF) are available. The model is in good agreement with
these MDF along the minor axis if we assume that the main bar has a mean solar
metallicity and the second thicker population has a lower metallicity. It then
creates naturally a vertical metallicity gradient by the mixing of the two
poulations. (abridged)
