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We combine far-infrared photometry from Herschel (PEP/HERMES) with deepmid-infrared spectroscopy from Spitzer to investigate the nature and the massassembly history of a sample of 31 Luminous and Ultraluminous Infrared Galaxiesat z~1 and 2 selected in GOODS-S with 24 $\mu$m fluxes between 0.2 and 0.5 mJy.We model the data with a self-consistent physical model (GRASIL) which includesa state-of-the-art treatment of dust extinction and reprocessing. We find thatall of our galaxies appear to require massive populations of old (>1 Gyr) starsand, at the same time, to host a moderate ongoing activity of SF (SFR < 100M$_{\odot}$/yr). The bulk of the stars appear to have been formed a few Gyrbefore the observation in essentially all cases. Only five galaxies of thesample require a recent starburst superimposed on a quiescent star formationhistory (SFH). We also find discrepancies between our results and those basedon optical-only SED fitting for the same objects; by fitting their observedSpectral Energy Distributions with our physical model we find higherextinctions (by $\Delta$A_{V} ~ 0.81 and 1.14) and higher stellar masses (by$\Delta$Log(M*) ~ 0.16 and 0.36 dex) for z~1 and z~2 (U)LIRGs, respectively.The stellar mass difference is larger for the most dust obscured objects. Wealso find lower SFRs than those computed from L_{IR} using the Kennicuttrelation due to the significant contribution to the dust heating byintermediate-age stellar populations through 'cirrus' emission (~73% and ~66%of total L_{IR} for z~1 and z~2 (U)LIRGs, respectively).

The complex physics of dusty star-forming galaxies at high redshifts as revealed by Herschel and Spitzer