A two-phonon version of the relativistic quasiparticle time-blocking approximation introduces a new class of many-body models for nuclear structure calculations based on the covariant energy density functional. As a fully consistent extension of the relativistic quasiparticle random phase approximation, the relativistic two-phonon model implies fragmentation of nuclear states over two-quasiparticle and two-phonon configurations coupled to each other. In particular, we show how the lowest two-phonon 1− state, identified as a member of the [2+ ⊗ 3−] quintuplet, emerges from the coherent two-quasiparticle pygmy dipole mode in vibrational nuclei. The inclusion of the two-phonon configurations into the model space allows a quantitative description of the positions and the reduced transition probabilities of the lowest 1− states in tin isotopes 112, 116, 120, 124Sn as well as the low-energy fraction of the dipole strength below the giant dipole resonance without any adjustment procedures. The model is applied to th