The mechanical/thermal/electrical properties on-demand design of CNTs-reinforced nanocomposites is a key scientific issue that limits the development of new-generation smart nanomaterials, and the establishment of a corresponding unified theoretical prediction model for the mechanical/thermal/electrical properties is the foundation of nanocomposites. Based on the equivalent medium theory (EMT) obtained by Maxwell far-field matching, a unified mechanical/thermal/electrical modified EMT model is established by introducing Young’s modulus, thermal conductivity, and electrical conductivity to the thin filler–matrix’s interlayer. According to literature, the proposed model was employed to theoretically calculate the variations in the overall Young’s modulus, thermal conductivity, and electrical conductivity of CNTs-reinforced nanocomposites with respect to the volume concentration of CNT fillers. Then, the applicability of the proposed theoretical model was validated in comparison with the experimental measurements. Numerical calculations showed that the interface is a key factor affecting the mechanical/thermal/electrical properties of CNTs-reinforced nanocomposites, and strengthening the interfacial effect is an effective way to enhance the overall properties of nanocomposites. In addition, the aspect ratio of CNT fillers also significantly affects the material properties of the CNT fillers interface phase and the CNTs-reinforced nanocomposites. By fitting the experimental data, the calculation expressions of the aspect ratios of CNT fillers on the Young’s modulus, thermal conductivity, and electrical conductivity of the CNT fillers interfacial phase are quantitatively given, respectively.