In one embodiment, a multi-layer insulation (MLI) composite material includes a first thermally-reflective layer and a second thermally-reflective layer spaced from the first thermally-reflective layer. At least one of the first or second thermally-reflective layers includes bandgap material that is reflective to infrared electromagnetic radiation. A region between the first and second thermally-reflective layers impedes heat conduction between the first and second thermally-reflective layers. Other embodiments include a storage container including a container structure that may be at least partially formed from such MLI composite materials, and methods of using such MLI composite materials.