We study WW and WZ production with $l\nu q{q}$ ($l=e,\mu$) final states using data collected by the D0 detector at the Fermilab Tevatron Collider corresponding to 4.3 fb^-1 of integrated luminosity from p-pbar collisions at sqrt{s}=1.96 TeV. Assuming the ratio between the production cross sections $\sigma(WW)$ and $\sigma(WZ)$ as predicted by the standard model, we measure the total WV (V=W,Z) cross section to be $\sigma(WV)= 19.6^{+3.2}_{-3.0}$ pb, and reject the background-only hypothesis at a level of 7.9 standard deviations. We also use b-jet discrimination to separate the WZ component from the dominant WW component. Simultaneously fitting WW and WZ contributions, we measure $\sigma(WW) = 15.9^{+3.7}_{-3.2}$ pb and $\sigma(WZ) = 3.3^{+4.1}_{-3.3}$ pb, which is consistent with the standard model predictions.