We present a measurement of the WW+WZ production cross section observed in a final state consisting of an identified electron or muon, two jets, and missing transverse energy. The measurement is carried out in a data sample corresponding to up to 4.6  fb−1 of integrated luminosity at s√=1.96  TeV collected by the CDF II detector. Matrix element calculations are used to separate the diboson signal from the large backgrounds. The WW+WZ cross section is measured to be 17.4±3.3  pb in agreement with standard model predictions. A fit to the dijet invariant mass spectrum yields a compatible cross section measurement.