An extension of the RPA approach to include both 1p1h⊗phonon configurations and the single-particle continuum in a unified framework has been done using the consistent Green-function formalism. The microscopic calculations of the giant E1 resonance in ⁴⁰Ca, ⁴⁸Ca and ²⁰⁸Pb have been performed in the 1p1h + 2p2h + continuum approximation developed here. A reasonable agreement with experiment, including a description of the widths, has been obtained. We underesti- mate the experimental width values by 14% for ⁴⁰Ca, 11% for ⁴⁸Ca and 4% for ²⁰⁸Pb.