Using 10 095 galaxies ( B < 20 mag ) from the Millennium Galaxy Catalogue , we derive B -band luminosity distributions and selected bivariate brightness distributions for the galaxy population subdivided by : eyeball morphology ; Sérsic index ( n ) ; 2dFGRS \eta -parameter ; rest- ( u - r ) colour ( global and core ) ; MGC continuum shape ; half-light radius ; ( extrapolated ) central surface brightness ; and inferred stellar mass-to-light ratio . All subdivisions extract highly correlated sub-sets of the galaxy population which consistently point towards two overlapping distributions : an old , red , inert , predominantly luminous , high central-surface brightness subset ; and a young , blue , star-forming , intermediate surface brightness subset . A clear bimodality in the observed distribution is seen in both the rest- ( u - r ) colour and \log ( n ) distributions . Whilst the former bimodality was well established from SDSS data ( 105 ) , we show here that the rest- ( u - r ) colour bimodality becomes more pronounced when using the core colour as opposed to global colour . The two populations are extremely well separated in the colour-log ( n ) plane . Using our sample of 3 314 ( B < 19 mag ) eyeball classified galaxies , we show that the bulge-dominated , early-type galaxies populate one peak and the bulge-less , late-type galaxies occupy the second . The early- and mid-type spirals sprawl across and between the peaks . This constitutes extremely strong evidence that the fundamental way to divide the luminous galaxy population ( M _ { B _ { \mbox { \tiny \sc MGC } } } -5 \log h < -16 mag , i.e. , dwarfs not included ) is into bulges ( old red , inert , high concentration ) and discs ( young , blue , star-forming , low concentration ) and that the galaxy bimodality reflects the two component nature of galaxies and not two distinct galaxy classes . We argue that these two-components require two independent formation mechanisms/processes and advocate early bulge formation through initial collapse and ongoing disc formation through splashback , infall and merging/accretion . We calculate the B -band luminosity-densities and stellar-mass densities within each subdivision and estimate that the z \approx 0 stellar mass content in spheroids , bulges and discs is 35 \pm 2 per cent , 18 \pm 7 and 47 \pm 7 per cent respectively .