Printing-on-fabric is an affordable and practical method for creating self-actuated deployable surfaces: thin strips of plastic are deposited on top of a pre-stretched piece of fabric using a commodity 3D printer; the structure, once released, morphs to a programmed 3D shape. Several physics-aware modeling tools have recently been proposed to help designing such surfaces. However, existing simulators do not capture well all the deformations these structures can exhibit. In this work, we propose a new model for simulating printed-on-fabric composites based on a tailored bilayer formulation for modeling plastic-on-top-of-fabric strips, and an extended Saint-Venant–Kirchhoff material law for modeling the surrounding stretchy fabric. We show how to calibrate our model through a series of standard experiments. Finally, we demonstrate the improved accuracy of our simulator by conducting various tests.