The interstellar medium of the radio galaxy IC 5063 is highly perturbed by an AGN jet expanding in the gaseous disc of the galaxy. We model this interaction with relativistic hydrodynamic simulations and multiphase initial conditions for the interstellar medium and compare the results with recent observations. As the jets flood through the intercloud channels of the disc, they ablate, accelerate, and disperse clouds to velocities exceeding 400 km s(-1). Clouds are also destroyed or displaced in bulk from the central regions of the galaxy. Our models with jet powers of 10(44) and 10(45) erg s(-1) are capable of reproducing many of the observed features in the position velocity diagram of IC 5063, and confirm the notion that the jet is responsible for the strongly perturbed gas dynamics seen in the ionized, neutral, and molecular gas phases. In our simulations, we also see strong venting of the jet plasma perpendicular to the disc, which entrains clumps and diffuse filaments into the halo of the galaxy. Our simulations are the first 3D hydrodynamic simulations of the jet and interstellar matter of IC 5063.