Accurate tire-road friction coefficient (TRFC) is crucial for enhancing both the motion performance and safety of vehicles. In this article, a model-based learning approach, incorporating event-triggered cubature Kalman filtering (ETCKF) and extended Kalman neural network (EKFNet), is proposed for identifying TRFC. Firstly, an event-triggered mechanism is designed to assess whether measurement data is lost, and it is fused with the cubature Kalman filtering to construct an ETCKF for processing sensor data. Subsequently, these processed data are fed into a nonlinear tire model to compute normalized tire forces. Next, an EKFNet, composed of an EKF and a four-layer neural network, utilizes the tire force information and vehicle model for the estimation of TRFC. Multiple virtual experiment results demonstrate that the estimation performance of the model-based learning framework outperforms conventional extended Kalman filter and unscented Kalman filter. Furthermore, the proposed method is applicable not only to distributed drive electric vehicles but also to traditional fuel vehicles.