Origami composites have been extensively utilized in space structures with constrained payload volumes due to their capability to efficiently transform compact structures into larger surface area or volume configurations. The proposed origami composite incorporates hydrogen-rich benzoxazine polymers known for their high radiation shielding capability and ultra-high-molecular-weight polyethylene fibers known for their high ballistic performance, radiation shielding capability, and flexibility. The proposed origami composite and manufacturing method can enhance bonding strength by achieving precise origami shapes and utilizing the same matrix for both flexible and rigid components. Membrane sheets are manufactured at a low curing temperature to provide flexibility, while rigid facets are separately manufactured at a high curing temperature to increase rigidity. The integration of a polyimide protection layer significantly enhances space environment resistance and reduces mass loss due to atomic oxygen erosion. Despite a slight decrease in ballistic performance after exposure to space conditions, the proposed origami composite maintains superior ballistic performance compared to conventional space materials and conventional origami composites. Compared to existing origami composites or conventional space materials, the proposed origami composite exhibited superior radiation shielding performance. The laminated structure of the proposed origami composite can offer some solar radiation shielding capability. The proposed origami composite offers a multifunctional origami solution as a membrane-space shield material, fulfilling requirements for high ballistic performance, cosmic radiation shielding, solar radiative heat shielding, and space environmental resistance.