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We present measurements of the linear polarization amplitudes and the strong relative phases that describe the flavor-untagged decays Bd0 → J/ψK+0 and Bs0 → J/ψφ in the transversity basis. We also measure the mean lifetime τs of the Bd0 mass eigenstates and the lifetime ratio τs/τd. 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 i>Bd0 → J/ψK+0 decay.