Predicting user actions based on anonymous sessions is a challenge to general recommendation systems because the lack of user profiles heavily limits data-driven models. Recently, session-based recommendation methods have achieved remarkable results in dealing with this task. However, the upper bound of performance can still be boosted through the innovative exploration of limited data. In this paper, we propose a novel method, namely Intra-and Inter-session Interaction-aware Graph-enhanced Network, to take inter-session item-level interactions into account. Different from existing intra-session item-level interactions and session-level collaborative information, our introduced data represents complex item-level interactions between different sessions. For mining the new data without breaking the equilibrium of the model between different interactions, we construct an intra-session graph and an inter-session graph for the current session. The former focuses on item-level interactions within a single session and the latter models those between items among neighborhood sessions. Then different approaches are employed to encode the information of two graphs according to different structures, and the generated latent vectors are combined to balance the model across different scopes. Experiments on real-world datasets verify that our method outperforms other state-of-the-art methods.