In aspect-level sentiment classification (ASC), state-of-the-art models encode either syntax graphs or relation graphs to capture the local syntactic information or global relational information. Despite the advantages of syntax and relation graphs, they have respective shortages which are neglected, limiting the representation power in the graph modeling process. To resolve their limitations, we design a novel local-global interactive graph (LGIG), which marries their advantages by stitching the two graphs via interactive edges. To model this LGI graph, we propose a novel neural network termed DigNet, whose core module is the stacked local-global interactive (LGI) layers performing two processes: intragraph message passing (IGMP) and cross-graph message passing (CGMP). In this way, the local syntactic and global relational information can be reconciled as a whole in understanding the aspect-level sentiment. Concretely, we design two variants of LGIGs with different kinds of interactive edges and three variants of LGI layers. We conduct experiments on several public benchmark datasets and the results show that we outperform previous best scores by 3%, 2.32%, and 6.33% in terms of Macro- 1 n Lap14, Res14, and Res15 datasets, respectively, confirming the effectiveness and superiority of the proposed LGIG and DigNet.