We describe a first attempt to derive properties of the regular and turbulent Galactic magnetic field from multi-frequency polarimetric observations of the diffuse Galactic synchrotron background . A single-cell-size model of the thin Galactic disk is constructed which includes random and regular magnetic fields and thermal and relativistic electrons . The disk is irradiated from behind with a uniform partially polarized background . Radiation from the background and from the thin disk is Faraday rotated and depolarized while propagating through the medium . The model parameters are estimated from a comparison with 350 MHz observations in two regions at intermediate latitudes done with the Westerbork Synthesis Radio Telescope . We obtain good consistency between the estimates for the random and regular magnetic field strengths and typical scales of structure in the two regions . The regular magnetic field strength found is a few \mu G , and the ratio of random to regular magnetic field strength B _ { ran } / B _ { reg } is 0.7 \pm 0.5 , for a typical scale of the random component of 15 \pm 10 pc . Furthermore , the regular magnetic field is directed almost perpendicular to the line of sight . This modeling is a potentially powerful method to estimate the structure of the Galactic magnetic field , especially when more polarimetric observations of the diffuse synchrotron background at intermediate latitudes become available .