The quasiparticle time blocking approximation (QTBA) is presented as a model for the description of natural-parity excitations in open-shell nuclei. Most attention is paid to the question of the damping of the giant dipole resonance. Within the model pairing correlations, two-quasiparticle (2q), and 2q-phonon configurations are included. Thus the QTBA is an extension of the quasiparticle random phase approximation to include quasiparticle-phonon coupling. Calculational formulas are presented for the case of neutral natural-parity excitations in spherical nuclei. The main equations are written in the coordinate representation that allows to take into account single-particle continuum completely. The QTBA is applied to describe E1 photoabsorption cross sections in nuclei Sn116,120,124. It has been obtained that the 2q-phonon configurations provide noticeable fragmentation of the giant dipole resonance resulting in the appearance of a significant spreading width. The results are compared with available experimental data.