  We present the analysis of HST $J$- and $H$-band imaging for 29 galaxies on
the star-forming main sequence at $z\sim2$, which have Adaptive Optics VLT
SINFONI integral field spectroscopy from our SINS/zC-SINF program. The SINFONI
H$\alpha$ data resolve the on-going star-formation and the ionized gas
kinematics on scales of $1-2$ kpc; the near-IR images trace the galaxies'
rest-frame optical morphologies and distributions of stellar mass in old
stellar populations at a similar resolution. The global light profiles of most
galaxies show disk-like properties well described by a single S\'ersic profile
with $n\sim1$, with only $\sim15%$ requiring a high $n>3$ S\'ersic index, all
more massive than $10^{10}M_\odot$. In bulge+disk fits, about $40%$ of galaxies
have a measurable bulge component in the light profiles, with $\sim15%$ showing
a substantial bulge-to-total ratio $B/T\ge0.3$. This is a lower limit to the
frequency of $z\sim2$ massive galaxies with a developed bulge component in
stellar mass because it could be hidden by dust and/or outshined by a thick
actively star-forming disk component. The galaxies' rest-optical half-light
radii range between $1-7$ kpc, with a median of 2.1 kpc, and lie slightly above
the size-mass relation at these epochs reported in the literature. This is
attributed to differences in sample selection and definitions of size and/or
mass measurements. The $(u-g)_{rest}$ color gradient and scatter within
individual $z\sim2$ massive galaxies with $\ge10^{11}M_\odot$ are as high as in
$z=0$ low-mass, late-type galaxies, and are consistent with the high
star-formation rates of massive $z\sim2$ galaxies being sustained at large
galactocentric distances.
