Tensegrity is a network of bars and cables that maintains its structural integrity with tension present in its cables. Other than typical structural failure mechanisms, tensegrity may fail due to slacking of cables or buckling of bars. Reallife tensegrities are an assemblage of component modules. Large tensegrities require excessive computation for model-based structural health monitoring (SHM), which may sometimes make the problem ill-posed. Instead of the entire domain, only a substructure can be investigated explicitly. Substructures decouple the structure into independent components that can be monitored individually, provided the sub-domain interface is measured. Yet the integration of substructures within predictor-corrector model-based SHM algorithms needs special investigation from consistency, stability, and accuracy perspectives. To consider system uncertainties Bayesian filtering-based SHM approaches have been employed in this study. The need for interface measurement has been circumvented through an output injection approach. To increase computational efficiency, the domain decomposition approach is coupled with an interacting filtering-based approach that employs Ensemble Kalman filter (for state estimation) within an envelope of Particle filter (for health parameter estimation). This facilitates simultaneous estimation of state and parameters while enabling full parallelization capability. The proposed approach is tested on a six-stage tensegrity tower made of component simplex modules.