We present an analysis of exclusive charmless semileptonic B-meson decays based on 377 million BBbar pairs recorded with the BABAR detector at the Upsilon(4S) resonance. We select four event samples corresponding to the decay modes B0 to pi- l+ nu, B+ to pi0 l+ nu, B0 to rho- l+ nu, and B+ -> rho0 l+ nu, and find the measured branching fractions to be consistent with isospin symmetry. Assuming isospin symmetry, we combine the two B to pi l nu samples, and similarly the two B to rho l nu samples, and measure the branching fractions BF(B0 to pi- l+ nu) = (1.41 +- 0.05 +- 0.07) x 10^-4 and BF(B0 to rho- l+ nu) = (1.75 +- 0.15 +- 0.27) x 10^-4, where the errors are statistical and systematic. We compare the measured distribution in q^2, the momentum transfer squared, with predictions for the form factors from QCD calculations and determine the CKM matrix element |V_ub|. Based on the measured partial branching fraction for B to pi l nu in the range q^2 < 12 GeV^2 and the most recent LCSR calculations we obtain |V_ub| = (3.78 +- 0.13 +0.55-0.40) x 10^-3, where the errors refer to the experimental and theoretical uncertainties. From a simultaneous fit to the data over the full q^2 range and the FNAL/MILC lattice QCD results, we obtain |V_ub| = (2.95 +- 0.31) x 10^-3 from B to pi l nu, where the error is the combined experimental and theoretical uncertainty. Show Partial Abstract