Optical integral field spectroscopy (IFS), combined with Hubble Space Telescope (HST) WFPC imaging, was used to characterize the central regions of the Seyfert 1 radio galaxy 3C 120. We carried out the analysis of the data, deriving intensity maps of different emission lines and the continua at different wavelengths from the observed spectra. Applying a two-dimensional modeling to the HST images, we decoupled the nucleus and the host galaxy and analyzed the host morphology. The host is a highly distorted bulge-dominated galaxy, rich in substructures. We developed a new technique to model the IFS data extending the two-dimensional modeling (hereafter three-dimensional modeling). Using this technique, we separated the Seyfert nucleus and the host galaxy spectra and derived a residual data cube with spectral and spatial information of the different structures in 3C 120. Three continuum-dominated structures (named A, B, and C) and three other extended emission-line regions (EELRs, named E1, E2, and E3) are found in 3C 120, which does not follow the general behavior of a bulge-dominated galaxy. We also found shells in the central kiloparsec that may be remnants of a past merging event in this galaxy. The origin of E1 is most probably due to the interaction of the radio jet of 3C 120 with the intergalactic medium (Axon et al. 1989; Sánchez et al. 2004a). Structures A, B, and the shell at the southeast of the nucleus seem to correspond to a larger morphological clumpy structure that may be a tidal tail, a consequence of the past merging event. We found a bright EELR (E2) in the innermost part of this tidal tail, nearby the nucleus, which shows a high ionization level. The kinematics of the E2 region and its connection to the tidal tail suggest that the tail has channeled gas from the outer regions to the center.