Graph neural networks (GNNs) have been widely studied for handling graph-structured data. Neighborhood awareness, a mechanism for integrating context into graphs, plays a crucial role in learning node embeddings in GNNs. Existing methods typically perform neighborhood-aware steps only at the node or hop level, which limits their ability to learn edge-level semantic information. There are two main challenges in extending neighborhood awareness to the edge level: (1) designing a learning framework with message propagation of edge embeddings, which supports the construction of edge embeddings to capture pairwise node relationships and propagate messages to perceive local context, and (2) developing a fusion approach that bridges node and edge embedding spaces, thereby compressing edge-level structural information into node space to enhance the original neighborhood awareness. In this study, we propose an edge-level neighborhood awareness network (ELNA-Net) that integrates both node- and edge-level context for more comprehensive neighborhood awareness. Specifically, we use the Taylor interaction effect to construct explicit interactions between pairwise nodes, which approximates edge embeddings and captures intricate non-linear correlations. Furthermore, the adaptive edge-aware propagation module adopts a line graph to switch the roles of nodes and edges, revealing potential dependencies among neighboring edges and promoting neighborhood awareness. Finally, we propose a cross-mapping fusion approach to integrate node- and edge-level contexts within the graph convolution operator. Experimental results demonstrate that ELNA-Net achieves superior performance in semi-supervised node classification and link prediction, outperforming state-of-the-art models.