The luminous infrared galaxy Arp 299 (IC 694 + NGC 3690) is studied using optical integral field spectroscopy obtained with the INTEGRAL system, together with archival Hubble Space Telescope WFPC2 and NICMOS images. The stellar and ionized gas morphology shows λ-dependent variations due to the combined effects of the dust internal extinction and the nature and spatial distribution of the different ionizing sources. The two-dimensional ionization maps have revealed an off-nuclear conical structure of about 4 kpc in length, characterized by high-excitation conditions and a radial gradient in the gas electron density. The apex of this structure coincides with B1 region of NGC 3690, which in turn presents Seyfert-like ionization, high extinction, and a high velocity dispersion. These results strongly support the hypothesis that B1 is the true nucleus of NGC 3690, where an AGN is located. In the circumnuclear regions H II-like ionization dominates, while LINER-like ionization is found elsewhere. The Hα-emitting sources with ages from 3.3 to 7.2×106 yr, have masses of between 6 and 680×106 Msolar and contribute about 45% to the bolometric luminosity (extinction corrected). The ionized (Hα) and neutral (Na D) gas velocity fields show similar structure on scales of several hundred to about 1 kpc, indicating that these gas components are kinematically coupled. The kinematic structure is complex and on scales of about 0.2 kpc does not appear to be dominated by the presence of ordered, rotational motions. The large velocity dispersion measured in NGC 3690 indicates that this galaxy is the most massive of the system. The low velocity amplitude and dispersion of the interface suggest that the ionized gas is slowly rotating or in a close to quiescent phase. Based on observations with the William Herschel Telescope operated on the island of La Palma by the ING in the Spanish Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias. Based also on observations with the NASA-ESA Hubble Space Telescope, obtained at the Space Telescope and Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract number NAS5-26555.