Vacuum-forming is a common manufacturing technique for constructing thin plastic shell products by pressing heated plastic sheets onto a mold using atmospheric pressure. Vacuum-forming is ubiquitous in packaging and casing products in industry spanning fast moving consumer goods to connected devices. Integrating advanced functionality, which may include sensing, computation and communication, within thin structures is desirable for various next-generation interactive devices. Hybrid additive manufacturing techniques like thermoforming are becoming popular for prototyping freeform electronics given its design flexibility, speed and cost-effectiveness. In this paper, we present a new hybrid method for constructing thin, rigid and free-form interconnected surfaces via fused deposition modelling (FDM) 3D printing and vacuum-forming. While 3D printing a mold for vacuum-forming has been explored by many, utilising 3D printing to construct sheet materials has remains unexplored. 3D printing the sheet material allows embedding conductive traces within thin layers of the substrate, which can be vacuum-formed but remain conductive and insulated. We characterise the behaviour of the vacuum-formed 3D printed sheet, analyse the electrical performance of 3D printed traces after vacuum-forming, and showcase a range of examples constructed using the technique. We demonstrate a new design interface specifically for designing conformal interconnects, which allows designers to draw conductive patterns in 3D and export pre-distorted sheet models ready to be 3D printed.