The magnetic and kinematic configuration of sunspot penumbrae is investigated by performing an inversion of the Stokes profiles of three infrared lines at 1565 nm. We use a two-component model atmosphere to describe, at least to first order, the unresolved structure of the penumbra. The observed Stokes profiles are successfully fitted, including those exhibiting abnormal shapes. The results of the inversion are consistent with the idea that the penumbra is formed by almost horizontal flux tubes embedded in a more vertical background magnetic field, as proposed by Solanki & Montavon (cite{Sol93}). The tubes possess weaker fields than the background except in the very outer penumbra, and carry most of the Evershed flow. We characterize the radial variation of the magnetic field vector and the velocity vector in these atmospheric components. In the middle penumbra and beyond, the magnetic field and the flow in the tubes are seen to return to the solar surface. Everywhere in the penumbra, there is a perfect alignment of the magnetic field vector and the velocity vector in the component describing the penumbral flux tubes. We find that the Evershed flow is supercritical in many places of the outer penumbra, and supersonic at some locations near the outer sunspot boundary. Based on these inversions, we suggest that the azimuthal fluctuations in the average magnetic field inclination and strength inferred from simple one-component models are caused by fluctuations in the filling factor (i.e., the fractional area of the resolution element occupied by flux tubes), not by changes in the intrinsic magnetic and kinematic properties of the background or the flux-tube atmospheres. Also, we confirm the jump of magnetic field azimuth proposed by Müller et al. (cite{Mul02}) to explain the observed net circular polarization of infrared lines.