Structural design with multi-family triply periodic minimal surfaces (TPMS) is a meaningful work that can combine the advantages of different types of TPMS. However, very few methods consider the influence of the blending of different TPMS on structural performance, and the manufacturability of final structure. Therefore, this work proposes a method to design manufacturable microstructures with topology optimization (TO) based on spatially-varying TPMS. In our method, different types of TPMS are simultaneously considered in the optimization to maximize the performance of designed microstructure. The geometric and mechanical properties of the unit cells generated with TPMS, that is minimal surface lattice cell (MSLC), are analyzed to obtain the performance of different types of TPMS. In the designed microstructure, MSLCs of different types are smoothly blended with an interpolation method. To analyze the influence of deformed MSLCs on the performance of the final structure, the blending blocks are introduced to describe the connection cases between different types of MSLCs. The mechanical properties of deformed MSLCs are analyzed and applied in TO process to reduce the influence of deformed MSLCs on the performance of final structure. The infill resolution of MSLC within a given design domain is determined according to the minimal printable wall thickness of MSLC and structural stiffness. Both numerical and physical experimental results demonstrate the effectiveness of the proposed method.