The two-photon 1s22s2p3P0→1s2s21S0 transition in berylliumlike ions is investigated theoretically within a fully relativistic framework and a second-order perturbation theory. We focus our analysis on how electron correlation, as well as the negative-energy spectrum, can affect the forbidden E1M1 decay rate. For this purpose, we include the electronic correlation via an effective local potential and within a single-configuration-state model. Due to its experimental interest, evaluations of decay rates are performed for berylliumlike xenon and uranium. We find that the negative-energy contribution can be neglected at the present level of accuracy in the evaluation of the decay rate. On the other hand, if contributions of electronic correlation are not carefully taken into account, it may change the lifetime of the metastable state by up to 20%. By performing a fully relativistic jj-coupling calculation, we find a decrease of the decay rate by two orders of magnitude compared to nonrelativistic LS-coupling calculations, for the selected heavy ions.