We present measurements of the lifetimes and polarization amplitudes for B(0)(s)-->J/psiphi and B(0)(d)-->J/psiK(*0) decays. Lifetimes of the heavy and light mass eigenstates in the B(0)(s) system are separately measured for the first time by determining the relative contributions of amplitudes with definite CP as a function of the decay time. Using 203+/-15 B(0)(s) decays we obtain tau(L) = (1.05(+0.16)(-0.13) +/- 0.02) ps and tau(H) = (2.07(+0.58)(-0.46) +/- 0.03) ps. Expressed in terms of the difference DeltaGamma(s) and average Gamma(s), of the decay rates of the two eigenstates, the results are DeltaGamma(s)/Gamma(s) = (65(+25)(-33) +/- 1)% and DeltaGamma(s) = (0.47(+0.19)(-0.24) +/- 0.01) ps(-1).