We present a refined gravitational lens model of the four-image lens system B1608+656 based on new and improved observational constraints: (i) the three independent time-delays and flux-ratios from VLA observations, (ii) the radio-image positions from VLBA observations, (iii) the shape of the deconvolved Einstein Ring from optical and infrared HST images, (iv) the extinction-corrected lens-galaxy centroids and structural parameters, and (v) a stellar velocity dispersion, sigma_ap=247+-35 km/s, of the primary lens galaxy (G1), obtained from an echelle spectrum taken with the Keck--II telescope. The lens mass model consists of two elliptical mass distributions with power-law density profiles and an external shear, totaling 22 free parameters, including the density slopes which are the key parameters to determine the value of H_0 from lens time delays. This has required the development of a new lens code that is highly optimized for speed. The minimum-chi^2 model reproduces all observations very well, including the stellar velocity dispersion and the shape of the Einstein Ring. A combined gravitational-lens and stellar dynamical analysis leads to a value of the Hubble Constant of H_0=75(+7/-6) km/s/Mpc (68 percent CL; Omega_m=0.3, Omega_Lambda=0.7. The non-linear error analysis includes correlations between all free parameters, in particular the density slopes of G1 and G2, yielding an accurate determination of the random error on H_0. The lens galaxy G1 is ~5 times more massive than the secondary lens galaxy (G2), and has a mass density slope of gamma_G1=2.03(+0.14/-0.14) +- 0.03 (68 percent CL) for rho~r^-gamma, very close to isothermal (gamma=2). (Abridged)
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