A measurement of the inclusive WW+WZ diboson production cross section in proton-proton collisions is reported, based on events containing a leptonically decaying W boson and exactly two jets. The data sample, collected at root s = 7 TeV with the CMS detector at the LHC, corresponds to an integrated luminosity of 5.0 fb(-1). The measured value of the sum of the inclusive WW and WZ cross sections is sigma(pp -> WW + WZ) = 68.9 +/- 8.7 (stat.) +/- 9.7 (syst.) +/- 1.5 (lum.) pb, consistent with the standard model prediction of 65.6 +/- 2.2 pb. This is the first measurement of WW+WZ production in pp collisions using this signature. No evidence for anomalous triple gauge couplings is found and upper limits are set on their magnitudes.