  We combine far-infrared photometry from Herschel (PEP/HERMES) with deep
mid-infrared spectroscopy from Spitzer to investigate the nature and the mass
assembly history of a sample of 31 Luminous and Ultraluminous Infrared Galaxies
at 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 includes
a state-of-the-art treatment of dust extinction and reprocessing. We find that
all of our galaxies appear to require massive populations of old (>1 Gyr) stars
and, at the same time, to host a moderate ongoing activity of SF (SFR < 100
M$_{\odot}$/yr). The bulk of the stars appear to have been formed a few Gyr
before the observation in essentially all cases. Only five galaxies of the
sample require a recent starburst superimposed on a quiescent star formation
history (SFH). We also find discrepancies between our results and those based
on optical-only SED fitting for the same objects; by fitting their observed
Spectral Energy Distributions with our physical model we find higher
extinctions (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. We
also find lower SFRs than those computed from L_{IR} using the Kennicutt
relation due to the significant contribution to the dust heating by
intermediate-age stellar populations through 'cirrus' emission (~73% and ~66%
of total L_{IR} for z~1 and z~2 (U)LIRGs, respectively).
