The joint estimation of system states and unknown input loads in dynamic civil structures, based on limited observations, has garnered significant attention in recent years. A widely used method for this is the augmented Kalman filter (AKF), which works by modeling system identification errors and measurement noise as Gaussian processes. However, the AKF is highly sensitive to the tuning of hyperparameters and to inaccuracies in the state-space model, which hampers its accuracy and robustness in practical applications. To address these challenges, this study proposes a neural network-assisted AKF (AKFNet) for joint input-state estimation. The AKFNet combines data-driven and model-driven approaches by incorporating a recurrent neural network (RNN) module into the AKF's recursive framework. The RNN module learns to refine the computation of the Kalman gain from real data, thereby enabling this approach to mitigate the limitations of traditional AKF methods in civil engineering, particularly the challenges posed by unknown noise covariances and model errors.