Aiming to optimize thin-walled composite structures commonly used in the aerospace industry, the concurrent optimization of stiffeners and layup angles in stiffened laminated composite structures is achieved by combining the Moving Morphable Component (MMC) method and the Shape Function with Penalization (SFP) method. Based on the proposed explicit topology optimization framework for stiffened laminate structures, optimization formulations for maximizing stiffness and maximizing fundamental natural frequency, considering additive manufacturing constraints, are proposed. An efficient numerical algorithm is established, with analytical sensitivity analysis results derived. The constraints considered include stiffener thickness limits and laminate layup requirements. In addition, by fully leveraging the larger design space of synergies between stiffeners and laminates, it is demonstrated that the design result obtained through concurrent optimization exhibits better structural performance than the stiffened laminate structures achieved through the sequential optimization of stiffener and laminate layup angles.