Electrical contact materials are generally Ag- or Cu-based composites and play a critical role in ensuring the reliability and efficiency of electrical equipments and electronic instruments. The MAX (M is an early transition metal, A is an element from III or IV main groups, and X is carbon or/and nitrogen) phase ceramics display a unique combination of properties and may serve as an ideal reinforcement phase for electrical contact materials. The biological materials evolved in nature generally exhibit three-dimensional (3D) interpenetrating-phase architectures, which may offer useful inspiration for the architectural design of electrical contact materials. Here, a series of bi-continuous Ag-Ti₃SiC₂ MAX phase composites with high ceramic contents exceeding 50 vol.% and having micron- and ultrafine-scaled 3D interpenetrating-phase architectures, wherein both constituents were continuous and mutually interspersed, were exploited by pressureless infiltration of Ag melt into partially sintered Ti₃SiC₂ scaffolds. The mechanical and electrical properties as well as the friction and wear performance of the composites were investigated and revealed to be closely dependent on the ceramic contents and characteristic structural dimensions. The composites exhibited a good combination of properties with high hardness over 2.3 GPa, high flexural strength exceeding 530 MPa, decent fracture toughness over 10 MPa·m^1/2, and good wear resistance with low wear rate at an order of 10⁻⁵ mm³/(N·m), which were much superior compared to the counterparts made by powder metallurgy methods. In particular, the hardness, electrical conductivity, strength, and fracture toughness of the composites demonstrated a simultaneous improvement as the structure was refined from micron- to ultrafine-scales at equivalent ceramic contents. The good combination of properties along with the facile processing route makes the Ag-Ti₃SiC₂ 3D interpenetrating-phase composites appealing for electrical contact applications.