The three-dimensional structure of an active region filament is studied using nonlinear force-free field extrapolations based on simultaneous observations at a photospheric and a chromospheric height. To that end, we used the Si I 10827 Å line and the He I 10830 Å triplet obtained with the Tenerife Infrared Polarimeter at the Vacuum Tower Telescope (Tenerife). The two extrapolations have been carried out independently from each other and their respective spatial domains overlap in a considerable height range. This opens up new possibilities for diagnostics in addition to the usual ones obtained through a single extrapolation from, typically, a photospheric layer. Among those possibilities, this method allows the determination of an average formation height of the He I 10830 Å signal of ≈2 Mm above the surface of the Sun. It allows, as well, a cross-check of the obtained three-dimensional magnetic structures to verify a possible deviation from the force-free condition, especially at the photosphere. The extrapolations yield a filament formed by a twisted flux rope whose axis is located at about 1.4 Mm above the solar surface. The twisted field lines make slightly more than one turn along the filament within our field of view, which results in 0.055 turns Mm-1. The convex part of the field lines (as seen from the solar surface) constitutes dips where the plasma can naturally be supported. The obtained three-dimensional magnetic structure of the filament depends on the choice of the observed horizontal magnetic field as determined from the 180° solution of the azimuth. We derive a method to check for the correctness of the selected 180° ambiguity solution.