We combine in a self-consistent way the constraints from both gravitational lensing and stellar kinematics to perform a detailed investigation of the internal mass distribution, amount of dark matter, and dynamical structure of the 16 early-type lens galaxies from the Sloan Lens ACS Survey (SLACS Survey), at z = 0.08-0.33, for which both Hubble Space Telescope/Advanced camera for Surveys and NICMOS high-resolution imaging and Very Large Telescope VI-MOS integral-field spectroscopy are available. Based on this data set, we analyse the inner regions of the galaxies, that is, typically within one (three-dimensional) effective radius r(e), under the assumption of axial symmetry and by constructing dynamical models supported by two-integral stellar distribution functions. For all systems, the total mass density distribution is found to be well approximated by a simple power law rho(tot) proportional to m(-gamma)' (with m being the ellipsoidal radius): this profile is on average slightly super-isothermal, with a logarithmic slope = 2.074(-0.041)(+0.043) (errors indicate the 68 per cent confidence interval) and an intrinsic scatter sigma(gamma)' = 0.144-(+0.055)(0.014), and is fairly round, with an average axial ratio <q > = 0.77 +/- 0.04. The lower limit for the dark matter fraction (f(DM)) inside r(e) ranges, in individual systems, from nearly zero to almost a half, with a median value of 12 per cent. By including stellar masses derived from stellar population synthesis models with a Salpeter initial mass function (IMF), we obtain an average f(DM) = 31 per cent, and the corresponding stellar profiles are physically acceptable, with the exception of two cases where they only marginally exceed the total mass profile. f(DM) rises to 61 per cent if, instead, a Chabrier IMF is assumed. For both IMFs, the dark matter fraction increases with the total mass of the galaxy (correlation significant at the 3 sigma level). Based on the intrinsic angular momentum parameter calculated from our models, we find that the galaxies can be divided into two dynamically distinct groups, which are shown to correspond to the usual classes of the (observationally defined) slow and fast rotators. Overall, the SLACS systems are structurally and dynamically very similar to their nearby counterparts, indicating that the inner regions of early-type galaxies have undergone little, if any, evolution since redshift z approximate to 0.35.