In this work, a hybrid topology optimization scheme based on the moving morphable component (MMC) method is presented for the design of stiffened membrane structure. The stiffened membrane structure is composed of a base membrane, reinforcing stiffeners, and functional cells. For an accurate and effective simulation of the structure, a hybrid structure model with multiple element types is constructed. In this study, MMC components used as the basic elements for the topology description will include several different types: bar elements for the stiffeners and continuum elements for the base membrane and functional cells. The base membrane is modeled using bi-modulus material. With this approach, the distribution of element types in different parts can be changed as the components are moved around during the optimization process. Some numerical examples are presented to validate the effectiveness of the proposed scheme.