Current asphalt pavement structural design methods often lack a strong quantitative link to materials’ mixtures and mechanical properties and typically ignore the significant tensile–compressive disparities of materials, resulting in notable analysis errors. This study employed the dual-modulus theory to numerically analyze flexible base asphalt pavements under varied configurations, revealing how critical structural responses and fatigue life evolve. This examination also determined optimal layer mixes through mechanical parameter modeling for integrated material–structure design. The results showed that fundamental responses and fatigue life vary nonlinearly with thickness and modulus. The effect of modulus outweighed that of thickness, with the effects of the tensile modulus being more pronounced than compressive ones, and surface transverse strain being most sensitive to both. The recommended compressive–tensile modulus ratios were about 1.5, 2.0, and 1.2 for upper, lower, and base layers, respectively. By using this integrated design method, the optimized pavement structures achieved superior stress distribution, significantly extending the base service life. As a result, more realistic design lifetimes were obtained.