We present the bivariate brightness distribution (BBD) for the 2dF Galaxy Redshift Survey (2dFGRS) based on a preliminary subsample of 45 000 galaxies. The BBD is an extension of the galaxy luminosity function, incorporating surface brightness information. It allows the measurement of the local luminosity density, jB, and of the galaxy luminosity and surface brightness distributions, while accounting for surface brightness selection biases. The recovered 2dFGRS BBD shows a strong luminosity-surface brightness relation [MB ∝ (2.4±1.50.5)μe], providing a new constraint for galaxy formation models. In terms of the number density, we find that the peak of the galaxy population lies at MB > -16.0 mag. Within the well-defined selection limits (-24 < MB < -16.0mag, 18.0 < μe < 24.5 mag arcsec-2) the contribution towards the luminosity density is dominated by conventional giant galaxies (i.e., 90 per cent of the luminosity density is contained within -22.5 < M < -17.5, 18.0 < μe < 23.0). The luminosity-density peak lies away from the selection boundaries, implying that the 2dFGRS is complete in terms of sampling the local luminosity density, and that luminous low surface brightness galaxies are rare. The final value we derive for the local luminosity density, inclusive of surface brightness corrections, is jB = 2.49 ± 0.20 × 108 h100 L⊙ Mpc-3. Representative Schlechter function parameters are M* = -19.75 ± 0.05, φ* = 2.02 ± 0.02 × 10-2 and α = -1.09 ± 0.03. Finally, we note that extending the conventional methodology to incorporate surface brightness selection effects has resulted in an increase in the luminosity density of -37 per cent. Hence surface brightness selection effects would appear to explain much of the discrepancy between previous estimates of the local luminosity density.