We report two complementary measurements of the WW + WZ cross section in the final state consisting of an electron or muon, missing transverse energy, and jets, performed using pp collision data at square root of s = 1.96 TeV collected by the CDF II detector. The first method uses the dijet invariant mass distribution while the second more sensitive method uses matrix-element calculations. The result from the second method has a signal significance of 5.4sigma and is the first observation of WW + WZ production using this signature. Combining the results gives sigma(WW + WZ) = 16.0 +/- 3.3 pb, in agreement with the standard model prediction.