We present measurements of the linear polarization amplitudes and the strong relative phases that describe the flavor-untagged decays Bd0-->J/psiK*0 and Bs0-->J/psiphi in the transversity basis. We also measure the mean lifetime taus of the Bs0 mass eigenstates and the lifetime ratio taus/taud. The analyses are based on approximately 2.8 fb(-1) of data recorded with the D0 detector. From our measurements of the angular parameters we conclude that there is no evidence for a deviation from flavor SU(3) symmetry for these decays and that the factorization assumption is not valid for the Bd0-->J/psiK*0 decay.