This paper proposes a novel Neural Lyapunov method-based transient stability assessment framework for power electronics-interfaced networked microgrids. The assessment framework aims to determine the large-signal stability of the networked microgrids and to characterize the disturbances that can be tolerated by the networked microgrids. The challenge of such assessment is how to construct a behavior-summary function for the nonlinear networked microgrids. By leveraging strong representation power of neural network, the behavior-summary function, i.e., a Neural Lyapunov function, is learned in the state space. A stability region is estimated based on the learned Neural Lyapunov function, and it is used for characterizing disturbances that the networked microgrids can tolerate. The proposed method is tested and validated in a grid-connected microgrid, three networked microgrids with mixed interface dynamics, and the IEEE 123-node feeder. Case studies suggest that the proposed method can address networked microgrids with heterogeneous interface dynamics, and in comparison with conventional methods that are based on quadratic Lyapunov functions, it can characterize the stability regions with much less conservativeness.