In the realm of modern recommender systems, user-item interaction data often exhibit sequential patterns in relation to various behaviors, such as clicks and purchases on e-commerce platforms. The objective of heterogeneous sequential recommendation (HSR) is to predict each user's next item of interest under a specific behavior based on these interactions. However, existing approaches to HSR struggle to fully capture item transition relationships, as they consider these relationships from a single dimension and at a coarse-grained level. To bridge this gap, we propose the novel Behavior-enhanced Long- and Short-term Interest (BLSI) model, which explores fine-grained item transition relationships in both local and global dimensionalities. At its core, BLSI incorporates a behavior-enhanced self-attention network (BSAN) to capture short-term user preferences. BSAN distinguishes the effects of different behaviors and considers cross-type behavior influences during the linear projection and attention score calculation stages. Additionally, BLSI employs a heterogeneous graph neural network (HGNN) to model long-term user interests by discriminatively aggregating the information of neighboring nodes according to their behavior transition relationships. Furthermore, a gating mechanism is implemented to adaptively fuse short- and long-term preferences for personalized recommendations. Extensive experimental results on three datasets demonstrate that BLSI significantly outperforms state-of-the-art recommendation methods, highlighting the advantages of leveraging sequentiality and behavioral heterogeneity.