The surface metallization of Si3N4 ceramics with the Ag–Cu conductive paste containing CuO was systematically investigated. The interfacial reactions between CuO and Si3N4 promoted the surface metallization of the ceramic substrate in an argon atmosphere. The effects of Ag and Cu relative contents on the evolution of the thick film surface morphology were studied. The electrical properties and tensile strength of composite ceramic substrates were enhanced through the generation of Ag–Cu eutectic solution within the thick film layer. The effect of brazing time on the properties of Ag–Cu/Si3N4 composite ceramic substrates was investigated. Mechanical testing and scanning electron microscopy (SEM) were used to analyze the interface tensile strength of the Ag–Cu/Si3N4 composite substrates and the morphology of the Ag–Cu film, and the bonding mechanism of the composite ceramic substrate was studied. When the sample was brazed at 800 °C for 20 min, the maximum tensile strength of 23.6 MPa between the Ag–Cu film and ceramic substrate was obtained, the lowest resistivity of 6.22 μΩ•cm was obtained. The bonding interface between thick film layer and the ceramic substrate formed the Ag–Cu mechanical structure was benefit for improving the comprehensive performance of the Cu/Si3N4 composite ceramic substrate.