As global demand for renewable energy continues to grow, high-altitude wind energy, characterized by high speed, wide distribution, and strong stability, has emerged as a promising alternative to low-altitude wind energy. Airborne Wind Energy systems (AWEs) are key to harnessing high-altitude wind, and Ground-Generator (Ground-Gen) AWEs are favored for their lower costs and simpler deployment. This study focuses on the umbrella–ladder-type Ground-Gen AWEs, aiming to address the research gap by exploring the influence of canopy permeability on the aerodynamic and structural response characteristics of flexible wind-capturing umbrellas. A single-umbrella model of the high-altitude wind-capturing umbrella was established, and bidirectional fluid–structure interaction (FSI) numerical simulations were conducted using the Arbitrary Lagrangian–Eulerian (ALE) method. Simulations were performed under a 30° angle of attack with two canopy thicknesses (5 × 10⁻⁵ m and 1 × 10⁻⁴ m) and varying permeability (adjusted via viscosity coefficient a and inertial coefficient b). Results showed that higher permeability (smaller a and b) hindered upper canopy inflation, while lower permeability promoted full inflation and more uniform stress distribution. The max/min in-plane shear stress for the model with the lowest permeability (Model F) was approximately 85% lower than that of the model with the highest permeability (Model A). The tension coefficient increased with decreasing permeability. Full inflation resulted in a slightly higher axial load in the upper suspension lines due to the lift force, with a difference of up to 92.3% during slight collapse. This difference becomes significantly more pronounced during severe collapse. Asymmetric flow fields at a 30° attack angle generated a lift force, resulting in higher tension coefficients than those at a 0° attack angle. These findings provide valuable references for the design and optimization of high-altitude wind-capturing umbrellas.