Ceramic/metal composite materials were widely used in national defense, military industry, and aerospace fields as lightweight impact-resistant structures with high specific strength and high energy absorption efficiency. With the development of 3D printing technology, it has become possible to fabricate complex lattice structures based on triply periodic minimal surfaces (TPMS). In this paper, an interpenetrating TPMS ballistic composite structure composed of silicon carbide (SiC) ceramic and titanium alloy (TC4) is designed. A series of numerical simulations are carried out under single-projectile and double-projectile penetration conditions using ABAQUS software. The damage modes, penetration depth, and ballistic limit velocity of the proposed structure and pure SiC target plate are compared and analyzed. The simulation results show that different interpenetrating TPMS structures exhibit distinct damage and failure modes. The three-dimensional topological configuration restrains crack propagation inside the ceramic, resulting in slighter overall damage than the pure SiC target plate. The damage caused by the second projectile further propagates along the penetration region of the first projectile, and accompanied by an increase in penetration depth. Compared with the pure SiC target plate, the three interpenetrating TPMS targets present smaller penetration depth and higher ballistic limit velocity. When the projectile can perforate the target plate, the primitive (P-type) structure shows better ballistic performance against low-velocity projectiles, while the diamond (D-type) structure is superior against high-velocity projectiles. It is demonstrated that the interpenetrating TPMS targets possess better ballistic performance than pure SiC at the same area density. The technical support and theoretical basis can be provided for the design of novel lightweight ceramic armor in this study.