The authors present the first measurement of the top quark mass using simultaneously data from two decay channels. They use a data sample of (square root)s = 1.96 TeV collisions with integrated luminosity of 1.9 fb−1 collected by the CDF II detector. They select dilepton and lepton + jets channel decays of t{bar t} pairs and reconstruct two observables in each topology. They use non-parametric techniques to derive probability density functions from simulated signal and background samples. The observables are the reconstructed top quark mass and the scalar sum of transverse energy of the event in the dilepton topology and the reconstructed top quark mass and the invariant mass of jets from the W boson decay in lepton + jets channel. They perform a simultaneous fit for the top quark mass and the jet energy scale which is constrained in situ by the hadronic W boson resonance from the lepton + jets channel. Using 144 dilepton candidate events and 332 lepton + jets candidate events they measure: M{sub top} = 171.9 ± 1.7 (stat. + JES) ± 1.1 (other sys.) GeV/c2 = 171.9 ± 2.0 GeV/c2. The measurement features a robust treatment of the systematic uncertainties, correlated between the two channels and develops techniques for a future top quark mass measurement simultaneously in all decay channels. Measurements of the W boson mass and the top quark mass provide a constraint on the mass of the yet unobserved Higgs boson. The Higgs boson mass implied by measurement presented here is higher than Higgs boson mass implied by previously published, most precise CDF measurements of the top quark mass in lepton + jets and dilepton channels separately.