Aims. We aim to determine the geometry, density gradient, and velocity structure of jets in post-asymptotic giant branch (post-AGB) binaries. Methods. Our high cadence time series of high-resolution optical spectra of jet-creating post-AGB binary systems provide us with a unique tomography of the jet. We determine the spatio-kinematic structure of the jets based on these data by fitting the synthetic spectral line profiles created by our model to the observed, orbital phase-resolved, Hα-line profiles of these systems. The fitting routine is provided with an initial spectrum and is allowed to test three configurations, derived from three specific jet launching models: a stellar jet launched by the star, an X-wind, and a disk wind configuration. We apply a Markov-chain Monte Carlo routine in order to fit our model to the observations. Our fitting code is tested on the post-AGB binary IRAS 19135+3937. Results. We find that a model using the stellar jet configuration gives a marginally better fit to our observations. The jet has a wide half-opening angle of about 76° and reaches velocities up to 870 km s⁻¹. Conclusions. Our methodology is successful in determining some parameters for jets in post-AGB binaries. The model for IRAS 19135+3937 includes a transparent, low density inner region (for a half-opening angle < 40°). The source feeding the accretion disk around the companion is most likely the circumbinary disk. We will apply this jet fitting routine to other jet-creating post-AGB stars in order to provide a more complete description of these objects.