Abstract: We present an analysis of exclusive charmless semileptonic B-meson decays based on 377 x 10(6) B (B) over bar pairs recorded with the BABAR detector at the Y(4S) resonance. We select four event samples corresponding to the decay modes B-0 -> pi(-)l(+)v, B+ -> pi(0)l(+)v, B-0 -> rho(-)l(+)v, and B+ -> rho(0)l(+)v and find the measured branching fractions to be consistent with isospin symmetry. Assuming isospin symmetry, we combine the two B -> pi lv samples, and similarly the two B -> rho lv samples, and measure the branching fractions B(B-0 -> pi(-)l(+)v) = (1.41 +/- 0.05 +/- 0.07) x 10(-4) and B(B-0 -> rho(-)l(+)v) = (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 Cabibbo-Kobayashi-Maskawa matrix element vertical bar V-ub vertical bar. Based on the measured partial branching fraction for B -> pi lv in the range q(2) < 12 GeV2 and the most recent QCD light-cone sum-rule calculations, we obtain vertical bar V-ub vertical bar = (3.78 +/- 0.13(-0.40)(+0.55)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 vertical bar V-ub vertical bar = (2.95 +/- 0.31) x 10(-3) from B -> pi lv, where the error is the combined experimental and theoretical uncertainty.