This paper presents the design of a two key-frame visual-inertial navigation system (2KF-VINS) using a combined Lie group extended Kalman filter (EKF) design framework. The conventional 2KF-VINS filter is unobservable for translations along all three axes and rotation about the gravity direction. As a result, the filter suffers from estimation inconsistencies related to unobservable transformations of the estimation problem. The proposed combined Lie group framework remedies this issue by implicitly preserving the observability consistency property of the filter. Monte Carlo numerical simulations are used to validate the theoretical performance of the 2KF-VINS, along with experimental validation using the EuRoC micro aerial vehicle (MAV) dataset to evaluate the performance in real-world scenarios. Additionally, the proposed algorithm is compared with state-of-the-art MSCKF, RI-MSCKF, , and 2KF-VINS versions with identical and realistic tuning parameters to validate the performance related to the accuracy, consistency, and computational speed of the method.