Multi-film containers for use in additive fabrication devices are provided. According to some aspects, a container may include multiple films that are at least partially detached from one another. In some embodiments, the multiple films may include films formed from different materials. As one example, an upper film may be formed so as to be relatively impermeable to substances within a source material of an additive fabrication device, whereas a lower film may be formed so as to provide desirable mechanical properties. In some cases, the multiple films may be commonly tensioned while being unattached to one another.