We present a measurement of the mass of the top quark using data corresponding to an integrated luminosity of 1.9  fb−1 of pp collisions collected at s√=1.96  TeV with the CDF II detector at Fermilab's Tevatron. This is the first measurement of the top quark mass using top-antitop pair candidate events in the lepton+jets and dilepton decay channels simultaneously. We reconstruct two observables in each channel and use a nonparametric kernel density estimation technique to derive two-dimensional probability density functions from simulated signal and background samples. The observables are the top quark mass and the invariant mass of two jets from the W decay in the lepton+jets channel, and the top quark mass and the scalar sum of transverse energy of the event in the dilepton channel. We perform a simultaneous fit for the top quark mass and the jet energy scale, which is constrained in situ by the hadronic W boson mass. Using 332 lepton+jets candidate events and 144 dilepton candidate events, we measure the top quark mass to be Mtop=171.9±1.7(stat+JES)±1.1(other syst)  GeV/c2=171.9±2.0  GeV/c2.