We present deep and high-resolution Hubble Space Telescope NIC2 F160W imaging at 1.6 Delta *mm of six z ~ 2 star-forming galaxies with existing near-infrared integral field spectroscopy from SINFONI at the Very Large Telescope. The unique combination of rest-frame optical imaging and nebular emission-line maps provides simultaneous insight into morphologies and dynamical properties. The overall rest-frame optical emission of the galaxies is characterized by shallow profiles in general (Sersic index n < 1), with median effective radii of R e ~ 5 kpc. The morphologies are significantly clumpy and irregular, which we quantify through a non-parametric morphological approach, estimating the Gini (G), multiplicity ( Delta *V), and M 20 coefficients. The estimated strength of the rest-frame optical emission lines in the F160W bandpass indicates that the observed structure is not dominated by the morphology of line-emitting gas, and must reflect the underlying stellar mass distribution of the galaxies. The sizes and structural parameters in the rest-frame optical continuum and H Delta *a emission reveal no significant differences, suggesting similar global distributions of the ongoing star formation and more evolved stellar population. While no strong correlations are observed between stellar population parameters and morphology within the NIC2/SINFONI sample itself, a consideration of the sample in the context of a broader range of z ~ 2 galaxy types (K-selected quiescent, active galactic nucleus, and star forming; 24 Delta *mm selected dusty, infrared-luminous) indicates that these galaxies probe the high specific star formation rate and low stellar mass surface density part of the massive z ~ 2 galaxy population, with correspondingly large effective radii, low Sersic indices, low G, and high Delta *V and M 20. The combined NIC2 and SINFONI data set yields insights of unprecedented detail into the nature of mass accretion at high redshift.