Multilayer insulation (MLI) components are important parts of spacecraft, in which thin films are the core elements. The film thicknesses are generally small, between 10 and 30 μm, to reduce the weight of the spacecraft. During the launch of a spacecraft, there is a rapid drop in the internal pressure, which causes the internal gas to flow out rapidly through the component. The resulting fluid force may cause film damage and failure, thereby directly affecting the normal operation of the spacecraft. Therefore, the mechanical characteristics of the thin films under rapid decompression conditions were investigated during this study. Considering the effects of the flow field stress distributions on the films during the rapid decompression, a fluid–structure interaction (FSI) model for a component was first constructed. The results show that the stress is largest in the outlet film, which is the part of the overall structure most vulnerable to failure. Furthermore, the effects of the structural parameters of the component on the stresses in the different film layers were analyzed using the orthogonal experimental method. The results show that the film thickness had the largest influence, followed by the film hole diameter, the number of component layers, and finally the staggered hole distance. Finally, a structurally optimized design scheme for the component is proposed based on a parameter range analysis with respect to the maximum film stress. After optimization, the maximum stress of the thin film decreased by 97.6%. This research has practical engineering value for the structural design and optimization of MLI components.