Anticipating possible behaviors of traffic participants is an essential capability of autonomous vehicles. Many behavior detection and maneuver recognition methods only have a very limited prediction horizon that leaves inadequate time and space for planning. To avoid unsatisfactory reactive decisions, it is essential to count long-term future rewards in planning, which requires extending the prediction horizon. In this paper, we uncover that clues to vehicle behaviors over an extended horizon can be found in vehicle interaction, which makes it possible to anticipate the likelihood of a certain behavior, even in the absence of any clear maneuver pattern. We adopt a recurrent neural network (RNN) for observation encoding, and based on that, we propose a novel vehicle behavior interaction network (VBIN) to capture the vehicle interaction from the hidden states and connection feature of each interaction pair. The output of our method is a probabilistic likelihood of multiple behavior classes, which matches the multimodal and uncertain nature of the distant future. A systematic comparison of our method against two state-of-the-art methods and another two baseline methods on a publicly available real highway dataset is provided, showing that our method has superior accuracy and advanced capability for interaction modeling.