An architectural membrane structure preferably includes an aerogel material disposed, for example, between two outer layers. The aerogel can be in monolithic or granular form or can be present in an aerogel composite. A method for manufacturing an architectural membrane structure includes securing an insert, e.g., an aerogel blanket, composite or granular aerogel, between a first and second layer.The architectural membrane structure can be used as a tensioned panel in envelopes such as roofing, overhangs, canopies or in other architectural or structural fabric applications.