The spectrum of the cosmic diffuse background shows that infrared observations are crucial for understanding how galaxies evolve, due to the significant role that dust grains play in reprocessing stellar radiation, especially at high redshifts (z~1) when the universe was more dust-obscured. In order to determine the physical mechanisms of how this energy is produced, spectroscopic observations of dusty, IR-detected sources are needed to reliably constrain their spectral energy distribution and emission line properties, such as star formation rate, extinction, AGN contribution, and electron density. We will review the characteristics of ~520 optical (Keck-II/DEIMOS) and infrared (Keck-I/MOSFIRE) spectra in the AKARI/NEP-Deep field at intermediate redshift (median z~0.7, with 74% of the sources at z>0.5), which also contain a statistically significant sample of AGN. In addition, we will relate these properties to SED models with CIGALE with UV to FIR photometry, and discuss the PAH 7.7 micron luminosity as an SFR indicator.