Constructing lunar bases is crucial as lunar missions progress towards utilization and exploitation. The challenging lunar environment, with its unique characteristics and limited resources, requires special materials, structures, and construction methods. Inflatable structures offer great potential for lunar construction due to their advantages in transportation, stowage, construction, and reliability. This paper proposes a rigidizable inflatable lunar habitat that maintains its shape even after air leakage, enhancing safety, durability, and fixability. The membrane material adapts to different requirements during transportation, construction, and service, achieved through solid-state actuation of shape memory polymer (SMP) for stiffness variation, allowing multiple moves and ground tests. This work comprises three parts: 1) system: design concept and construction processes, 2) material: design and characterization of restraint and rigidization materials, and 3) structure: numerical validation of structure properties. Finite element analysis, based on material models obtained through dynamic mechanical analysis (DMA) and tensile tests, demonstrates the effectiveness of including an SMP rigidization layer in preventing collapse and enhancing dynamic properties. This paper not only proposes a new system, but also provides material design methods and requirements, along with structural validation techniques. Findings validate the feasibility of rigidizable inflatable lunar habitats, applicable in extreme environments, also in temporary buildings, space structures, and soft robotics.