Presented are deployable structures having multi-stable-state characteristics using skeletal architectures mounted onto textile backings, methods for making/using such structures, and vehicle components having bistable characteristics provided by polymeric exoskeletons printed onto textile substrates. A multi-stable-state deployable structure includes an elastic substrate fabricated from a (knitted) textile sheet, and an articulating (polymeric) framework mounted on the knitted textile sheet. The articulating framework and textile sheet structurally cooperate to transition from a first stable state, in which the deployable structure maintains a substantially planar shape, to a second stable state, in which the deployable structure maintains a first multidimensional topography, and from the second state to a third stable state, in which the deployable structure maintains a second multidimensional topography distinct from the first multidimensional topography. The articulating framework may include an elongated spine sandwiched between first and second sets of ribs, and a frame circumscribing the spine and ribs.