Two-photon E1M1 transition rates are evaluated for heliumlike ions with nuclear charges in the range Z = 50-94. The two-photon rates modify previously published lifetimes/transition rates of 2 3 P0 states. For isotopes with nuclear spin I = 0, where hyperfine quenching dominates the 2 3 P0 decay, two-photon contributions are significant; for example, in heliumlike 187 Os the two-photon correction is 3% of the total rate. For isotopes with I = 0, where the 2 3 P0 decay is unquenched, the E1M1 corrections are even more important reaching 60% for Z=94. Therefore, to aid in the interpretation of experiments on hyperfine quenching in heliumlike ions and to provide a more complete database for unquenched transitions, a knowledge of E1M1 rates is important.