  We present a novel method to retrieve the chemical structure of galaxies
using integral field spectroscopy data through the stellar Metallicity
Distribution Function (MDF). This is the probability distribution of observing
stellar populations having a metallicity $Z$. We apply this method to a set of
$550$ galaxies from the CALIFA survey. We present the behaviour of the MDF as a
function of the morphology, the stellar mass and the radial distance. We use
the stellar metallicity radial profiles retrieved as the first moment of the
MDF, as an internal test for our method. The gradients in these radial profiles
are consistent with the known trends: they are negative in massive early-type
galaxies and tend to positive values in less massive late-type ones. We find
that these radial profiles may not convey the complex chemical structure of
some galaxy types. Overall, low mass galaxies
($\log{M_\star/\mathrm{M}_{\odot}}\leq10$) have broad MDFs
($\sigma_Z\sim1.0\,$dex), with unclear dependence on their morphology. However
this result is likely affected by under-represented bins in our sample. On the
other hand, massive galaxies ($\log{M_\star/\mathrm{M}_{\odot}}\geq11$) have
systematically narrower MDFs ($\sigma_Z\leq0.2\,$dex). We find a clear trend
whereby the MDFs at $r_k/R_e>1.5$ have large variance. This result is
consistent with sparse SFHs in medium/low stellar density regions. We further
find there are multi-modal MDFs in the outskirts ($\sim18\,$per cent) and the
central regions ($\sim40\,$per cent) of galaxies. This behaviour is linked to a
fast chemical enrichment during early stages of the SFH, along with the
posterior formation of a metal-poor stellar population.
