We examine in this paper a stellar-mass-selected sample of galaxies at 1 < z < 3 within the Hubble Ultra Deep Field, utilizing Wide-Field Camera-3 (WFC3) imaging, to study the rest-frame optical morphological and structural distribution of galaxies at this epoch. We measure how apparent morphologies (disc, elliptical, peculiar) correlate with physical properties, such as quantitative structure and spectral type. One primary result is that apparent morphology does not correlate strongly with stellar populations, nor with galaxy structure at this epoch, suggesting a chaotic formation history for Hubble types at z > 1. By using a locally defined definition of disc and elliptical galaxies based on structure and spectral type, we find no true ellipticals at z > 2, and a fraction of 3.2 ± 2.3 per cent at 1.5 < z < 2. Local counterparts of disc galaxies are at a similar level of 7–10 per cent, much lower than the 75 per cent fraction at lower redshifts. We further compare WFC3 images with the rest-frame ultraviolet view of galaxies from ACS imaging, showing that galaxies imaged with the ACS, which appear peculiar, often contain an ‘elliptical’-like morphology in the WFC3. We show through several simulations that this larger fraction of elliptical-like galaxies is partially due to the courser point spread function of the WFC3, and that the ‘elliptical’ morphological class very likely includes early-type discs. We also measure the merger history for our sample using concentration, asymmetry and clumpiness parameters, finding a redshift evolution increasing with redshift, and a peak merger fraction of ∼30 per cent at z∼ 2 for the most massive galaxies with M* > 1010 M⊙, consistent with previous results from the ACS and NICMOS. We also compare our results to semi-analytical model results and find a relatively good agreement between our morphological breakdown and the predictions. We finally argue that galaxies classified visually as peculiar, elliptical or peculiar ellipticals, all have similar structural and stellar population properties, suggesting that these galaxies are in a similar formation mode, likely driven by major mergers.