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, j_B, and the galaxy luminosity and surface brightness distributions while accounting for surface brightness selection biases. The recovered 2dFGRS BBD shows a strong surface brightness-luminosity relation (M_B~2.4μ_e). The luminosity-density is dominated by normal galaxies and the luminosity-density peak lies away from the selection boundaries implying that the 2dFGRS is complete 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: j_B=2.49+/-0.20x10^8 h L_solar Mpc^-3. Representative Schechter function parameters are: M*=-19.75+/-0.05, phi*=2.02+/-0.02x10^-2 and alpha=-1.09+/-0.03. Extending the conventional methodology to incorporate surface brightness selection effects has resulted in an increase in the luminosity-density of 37%. ; Comment: Accepted for publication in MNRAS. 20 pages and 15 figures