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Real-time Hybrid Simulation (RTHS) is a technique wherein a structural system is divided into an analytical and an experimental substructure. The former is modeled numerically while the latter is physically present in the laboratory. The two substructures are kinematically linked together at their interface degrees of freedom (DOFs) and the equations of motion are solved in real-time to determine the structure’s response. One of the main challenges of RTHS is to include the effects of soil–foundation–structure interaction (SFSI), which can have a substantial effect on the overall response. The soil domain cannot be modeled experimentally due to the large payload size. On the other hand, modeling the soil domain numerically, using a continuum-based approach, in real-time is challenging due to the associated computational cost. To address these issues, this paper presents a framework for seismic RTHS of SFSI systems using a Neural Network (NN)-based macroelement model of the soil–foundation system. A coupled SFSI model is used to train the NN model and the loss function is based on dynamic equilibrium at the interface between the foundation and the structure. The framework is demonstrated using a three-story building with the lateral load resisting system comprised of moment resisting and damped brace frames. The proposed framework ensures a stable and accurate RTHS, accounting for SFSI by incorporating: (a) spring elements at the output DOFs of the NN model to remove rigid body modes; (b) dashpot elements at the output DOFs of the NN model to mitigate spurious higher frequencies of vibration; and (c) regularization in the NN model’s architecture with data augmentation to reduce overfitting.