The capillary component and adsorptive component of matric suction differently impact the soil strength. Due to the cavitation effects of pore water, the adsorption effect dominates the behavior of soil when matric suction exceeds the cavitation tension. Based on the binary medium theory, a compression-shear strength model for unsaturated soils considering both capillary effect and adsorption effect is established. Compared with test data, the proposed compression-shear strength model has better prediction performance on the compression-shear strength of soil over a range of wide suction. The soil failure depends both on tension-shear stress and compression-shear stress. The tension-shear coupling mechanism in the soil is first investigated. A concept of closed stress point is introduced to divide the two zones of tension-shear coupling stress and compression-shear stress. According to the compression-shear strength model and tension-shear failure mechanism, the tension-shear and compression-shear joint strength model applicable to plane stress conditions is then established. Compared with test data, the proposed model in this article can better predict the nonlinear strength characteristics of clays and has better applicability. Finally, using the user material subroutine (UMAT), the secondary development of the joint strength model is conducted in ABAQUS and then applied to the slope stability analysis. The calculation results show that the established strength model presents a reasonable description of the development of the tension-shear coupling plastic zone in slope and gives an accurate safety factor.