A {it Hubble Space Telescope} ({it HST}) / Advanced Camera for Surveys (ACS) study of the structural properties of 85 luminous and ultraluminous ($L_{rm IR} > 10^{11.4}$ L$_odot$) infrared galaxies (LIRGs and ULIRGs) in the Great Observatories All-sky LIRG Survey (GOALS) sample is presented. Two-dimensional GALFIT analysis has been performed on F814W {it I}-band images to decompose each galaxy, as appropriate, into bulge, disk, central PSF and stellar bar components. The fraction of bulge-less disk systems is observed to be higher in LIRGs (35%) than in ULIRGs (20%), with the disk+bulge systems making up the dominant fraction of both LIRGs (55%) and ULIRGs (45%). Further, bulge+disk systems are the dominant late-stage merger galaxy type and are the dominant type for LIRGs and ULIRGs at almost every stage of galaxy-galaxy nuclear separation. The mean {it I}-band host absolute magnitude of the GOALS galaxies is $-22.64pm$0.62 mag (1.8$^{+1.4}_{-0.4}$ L$^*_I$), and the mean bulge absolute magnitude in GOALS galaxies is about 1.1 magnitude fainter than the mean host magnitude. Almost all ULIRGs have bulge magnitudes at the high end (-20.6 to - 23.5 mag) of the GOALS bulge magnitude range. Mass ratios in the GOALS binary systems are consistent with most of the galaxies being the result of major mergers, and an examination of the residual-to-host intensity ratios in GOALS binary systems suggests that smaller companions suffer more tidal distortion than the larger companions. We find approximately twice as many bars in GOALS disk+bulge systems (32.8%) than in pure-disk mergers (15.9%) but most of the disk+bulge systems that contain bars are disk-dominated with small bulges. The bar-to-host intensity ratio, bar half-light radius, and bar ellipticity in GOALS galaxies are similar to those found in nearby spiral galaxies.(abridged)
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