We conduct spectral observations of 138 superthin galaxies (STGs) with high radial-to-vertical stellar disk scale ratios with the Dual Imaging Spectrograph on the 3.5m telescope at the Apache Point Observatory (APO) to obtain the ionized gas rotation curves with R~5000 resolution. We also performed near-infrared (NIR) H and Ks photometry for 18 galaxies with the NICFPS camera on the 3.5m telescope. The spectra, the NIR photometry, and published optical and NIR photometry are used for modeling that utilizes the thickness of the stellar disk and rotation curves simultaneously. The projection and dust extinction effects are taken into account. We evaluate eight models that differ in their free parameters and constraints. As a result, we estimated the masses and scale lengths of the galactic dark halos. We find systematic differences between the properties of our red and blue STGs. The blue STGs have a large fraction of dynamically underevolved galaxies whose vertical velocity dispersion is low in both gas and stellar disks. The dark halo-to-disk scale ratio is shorter in the red STGs than in the blue ones, but in a majority of all STGs, this ratio is under 2. The optical color (r-i) of the STGs correlates with their rotation curve maximum, vertical velocity dispersion in stellar disks, and mass of the dark halo. We conclude that there is a threshold central surface density of 50M_{sun}_/pc^2^ below which we do not observe very thin, rotationally supported galactic disks.