In this study, two-dimensional composite of Cu/Ni laminated and brick-mortar structures were explored utilizing the GTN constitutive model and mathematical plane tessellation schemes. Uniaxial and biaxial stretching behaviors were analyzed by precisely controlling the model microgeometries and phase volume fraction characteristics, using finite element numerical simulations. The results show that the laminated structure represented by the triangular tessellation models exhibits stretching-dominated deformation when uniaxial stretching is carried out along the direction of the hard phase laminae and shows outstanding strength. The brick-mortar structure represented by the triangular tessellation models undergoes deformation in a combination of bending and stretching (compression), which helps to improve the plasticity yet avoid a significant decrease in strength. In addition, as the volume fraction of hard phase increases, the overall strength increases, but the plasticity decreases. When the volume fraction of hard phase is higher, the laminated structure represented by the triangular tessellation model is more prominent in terms of strength, whereas when the volume fraction of hard phase is lower, the brick-mortar structure represented by the triangular tessellation model is more prominent in terms of plasticity. Under biaxial conditions, the quadrangular tessellation scheme for brick-mortar structures shows better overall strength and plasticity. By analysing the microstructure-mechanical properties relationship in a two-phase composites, this study provides guidance for material synthesis through structural patterning.