Integral field optical spectroscopy with the INTEGRAL fiber-fed system and Hubble Space Telescope optical imaging are used to map the complex stellar and warm ionized gas structure in the ultraluminous infrared galaxy IRAS 12112+0305. Images reconstructed from wavelength-delimited extractions of the integral field spectra reveal that the observed ionized gas distribution is decoupled from the stellar main body of the galaxy, with the dominant continuum and emission-line regions separated by projected distances of up to 7.5 kpc. The two optical nuclei are detected as apparently faint emission-line regions, and their optical properties are consistent with being dust-enshrouded weak [O I] LINERs. The brightest emission-line region is associated with a faint (mI=20.4), giant H II region of 600 pc diameter, in which a young (~5 Myr) massive cluster of about 2x107 Msolar dominates the ionization. Internal reddening toward the line-emitting regions and the optical nuclei ranges from 1 to 8 mag in the visual. Taking the reddening into account, the overall star formation in IRAS 12112+0305 is dominated by starbursts associated with the two nuclei and corresponds to a star formation rate of 80 Msolar yr-1. 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 Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc. under NASA contract number NAS5-26555.