  We present new results on the physical nature of infrared-luminous sources at
0.5<z<2.8 as revealed by HST/NICMOS imaging and IRS mid-infrared spectroscopy.
Our sample consists of 134 galaxies selected at 24\mum with a flux of S(24\mum)
> 0.9 mJy. We find many (~60%) of our sources to possess an important bulge
and/or central point source component, most of which reveal additional
underlying structures after subtraction of a best-fit sersic (or sersic+PSF)
profile. Based on visual inspection of the NIC2 images and their residuals, we
estimate that ~80% of all our sources are mergers. We calculate lower and upper
limits on the merger fraction to be 62% and 91% respectively. At z < 1.5, we
observe objects in early (pre-coalescence) merging stages to be mostly disk and
star formation dominated, while we find mergers to be mainly bulge-dominated
and AGN-starburst composites during coalescence and then AGN-dominated in late
stages. This is analogous to what is observed in local ULIRGs. At z \geq 1.5,
we find a dramatic rise in the number of objects in pre-coalescence phases of
merging, despite an increase in the preponderance of AGN signatures in their
mid-IR spectra and luminosities above 10^12.5 L_sun. We further find the
majority of mergers at those redshifts to retain a disk-dominated profile
during coalescence. We conclude that, albeit still driven by mergers, these
high-z ULIRGs are substantially different in nature from their local
counterparts and speculate that this is likely due to their higher gas content.
Finally, we observe obscured ({\tau}_{9.7\mum} > 3.36) quasars to live in faint
and compact hosts and show that these are likely high-redshift analogs of local
dense-core mergers. We find late-stage mergers to show predominantly unobscured
AGN spectra, but do not observe other morphological classes to occupy any one
specific region in the Spoon diagram. [abridged]
