Data assimilation (DA) is widely used as a data-driven system identification method, enhancing our understanding of the generative mechanisms in the observational data based on the identified model and its parameters. Due to this advantage, DA has gradually begun to be applied in neuroscience studies. Recently, we introduced a DA-based method for reconstructing the internal state of the brain using the neural mass model and human scalp electroencephalography (EEG). This method allows us to estimate the balance of synaptic interactions between excitatory and inhibitory neurons (E/I balance) in the brain only from observed EEG. Although we confirmed the neurophysiological validity of the proposed EEG-DA method in our recent works, this method cannot be applied to multivariate EEG signals to parallelly infer the E/I balance changes and underlying network dynamics. In this study, to address this issue, we proposed an extended version of our DA method specified to multivariate observed EEG signals. This method enables us to estimate sensor-level functional network and E/I balance changes of each EEG sensor in parallel. The method was validated by showing that it could parallelly estimate sensor-level network structures and E/I balance changes from synthetic multivariate EEG signals. The results of this study indicate that it has the potential to quantify how the E/I balance changes functionally affect the brain network dynamics.