The probabilities of two-photon decay for hydrogen (H) and antihydrogen (-H) atoms in the presence and absence of an external electric field are analytically calculated. In particular, the probabilities of the E1E2 and E1M1 transitions between the 2p and 1s levels are calculated for the case when emitted photons are characterized by polarization vectors and wavevectors. It is shown that, in an external electric field, the decay probabiities for 2s and 2p levels differ for H and-H atoms because of interference terms linear in field. Coulomb Green's function method is used for summing over intermediate states.