We introduce a method for modeling disk galaxies designed to take full advantage of data from integral field spectroscopy (IFS). The method fits equilibrium models to simultaneously reproduce the surface brightness, rotation and velocity dispersion profiles of a galaxy. The models are fully self-consistent 6D distribution functions for a galaxy with a Sersic-profile stellar bulge, exponential disk and parametric dark matter halo, generated by an updated version of GalactICS. By creating realistic flux-weighted maps of the kinematic moments (flux, mean velocity and dispersion), we simultaneously fit photometric and spectroscopic data using both maximum-likelihood and Bayesian (MCMC) techniques. We apply the method to a GAMA spiral galaxy (G79635) with kinematics from the SAMI Galaxy Survey and deep $g$- and $r$-band photometry from the VST-KiDS survey, comparing parameter constraints with those from traditional 2D bulge-disk decomposition. Our method returns broadly consistent results for shared parameters, while constraining the mass-to-light ratios of stellar components and reproducing the HI-inferred circular velocity well beyond the limits of the SAMI data. While the method is tailored for fitting integral field kinematic data, it can use other dynamical constraints like central fibre dispersions and HI circular velocities, and is well-suited for modelling galaxies with a combination of deep imaging and HI and/or optical spectra (resolved or otherwise). Our implementation (MagRite) is computationally efficient and can generate well-resolved models and kinematic maps in under a minute on modern processors.
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