We present an updated measurement of the B(s)(0) lifetime using the semileptonic decays B(s)(0)→D(s)(-)μ(+)νX, with D(s)(-)→ϕπ(-) and ϕ→K(+)K(-) (and the charge conjugate process). This measurement uses the full Tevatron Run II sample of proton-antiproton collisions at √[s]=1.96 TeV, comprising an integrated luminosity of 10.4 fb(-1). We find a flavor-specific lifetime τ(fs)(B(s)(0))=1.479±0.010(stat)±0.021(syst) ps. This technique is also used to determine the B(0) lifetime using the analogous B(0)→D(-)μ(+)νX decay with D(-)→ϕπ(-) and ϕ→K(+)K(-), yielding τ(B(0))=1.534±0.019(stat)±0.021(syst) ps. Both measurements are consistent with the current world averages, and the B(s)(0) lifetime measurement is one of the most precise to date. Taking advantage of the cancellation of systematic uncertainties, we determine the lifetime ratio τ(fs)(B(s)(0))/τ(B(0))=0.964±0.013(stat)±0.007(syst).