We present a two-dimensional multi-component photometric decomposition of 404 galaxies from the Calar Alto Legacy Integral Field Area data release 3 (CALIFA-DR3). They represent all possible galaxies with no clear signs of interaction and not strongly inclined in the final CALIFA data release. Galaxies are modelled in the g, r, and i Sloan Digital Sky Survey (SDSS) images including, when appropriate, a nuclear point source, bulge, bar, and an exponential or broken disc component. We use a human-supervised approach to determine the optimal number of structures to be included in the fit. The dataset, including the photometric parameters of the CALIFA sample, is released together with statistical errors and a visual analysis of the quality of each fit. The analysis of the photometric components reveals a clear segregation of the structural composition of galaxies with stellar mass. At high masses (log (M⋆/M⊙) > 11), the galaxy population is dominated by galaxies modelled with a single Sérsic or a bulge+disc with a bulge-to-total (B/T) luminosity ratio B/T > 0.2. At intermediate masses (9.5 < log (M⋆/M⊙) < 11), galaxies described with bulge+disc but B/T < 0.2 are preponderant, whereas, at the low mass end (log (M⋆/M⊙) < 9.5), the prevailing population is constituted by galaxies modelled with either purediscs or nuclear point sources+discs (i.e., no discernible bulge). We obtain that 57% of the volume corrected sample of disc galaxies in the CALIFA sample host a bar. This bar fraction shows a significant drop with increasing galaxy mass in the range 9.5 < log (M⋆/M⊙) < 11.5. The analyses of the extended multi-component radial profile result in a volume-corrected distribution of 62%, 28%, and 10% for the so-called Type I (pure exponential), Type II (down-bending), and Type III (up-bending) disc profiles, respectively. These fractions are in discordance with previous findings. We argue that the different methodologies used to detect the breaks are the main cause for these differences. The catalog of fitted parameters is only available at the CDS via anonymous ftp to http://cdsarc.u-strasbg.fr (http://130.79.128.5) or via http://cdsarc.u-strasbg.fr/viz-bin/qcat?J/A+A/598/A32