We present a new method to simultaneously/self-consistently model the mass distribution of galaxy clusters that combines constraints from strong lensing features, X-ray emission and galaxy kinematics measurements. We are able to successfully decompose clusters into their collisionless and collisional mass components thanks to the X-ray surface brightness, as well as using the dynamics of cluster members to obtain more accurate masses with the fundamental plane of elliptical galaxies. Knowledge from all observables is included through a consistent Bayesian approach in the likelihood or in physically motivated priors. We apply this method to the galaxy cluster Abell S1063 and produce a mass model that we publicly release with this paper. The resulting mass distribution presents a different ellipticities for the intra-cluster gas and the other large-scale mass components; and deviation from elliptical symmetry in the main halo. We assess the ability of our method to recover the masses of the different elements of the cluster using a mock cluster based on a simplified version of our Abell S1063 model. Thanks to the wealth of information provided by the mass model and the X-ray emission, we also found evidence for an on-going merger event with gas sloshing from a smaller infalling structure into the main cluster. In agreement with previous findings, the total mass, gas profile and gas mass fraction are consistent with small deviations from the hydrostatic equilibrium. This new mass model for Abell S1063 is publicly available as is the software used to construct it through the \textsc{Lenstool} package.