An advanced Neuro-space mapping (Neuro-SM) multiphysics parametric modeling approach for microwave passive components is proposed in this paper. The electromagnetic (EM) domain model, which represents the EM responses with respect to geometrical parameters, is regarded as a coarse model. The multiphysics domain model, which represents the multiphysics responses with respect to both geometrical parameters and multiphysics parameters, is regarded as a fine model. The proposed model is constructed by the input mapping, the output mapping and the coarse model. The input mapping is used to map multiphysics parameters to EM parameters. The output mapping is introduced to further narrow the gap between the output of the coarse model and the multiphysics data. In addition, a three-stage training method is proposed for efficiently developing the proposed multiphysics model. The proposed technique, which combines the efficiency of EM analysis and the accuracy of multiphysics analysis, can achieve better accuracy with less multiphysics data than existing modeling methods. The developed Neuro-SM multiphysics model provides accurate and fast predictions of multiphysics responses. Therefore, the design cycle of microwave passive components is shortened while the modeling cost is significantly reduced. Two microwave filter examples are utilized to demonstrate the accuracy of the proposed parametric modeling technique.