Class imbalance is pervasive in real-world graph datasets, where the majority of annotated nodes belong to a small set of classes (majority classes), leaving many other classes (minority classes) with only a handful of labeled nodes. Graph Neural Networks (GNNs) suffer from significant performance degradation in the presence of class imbalance, exhibiting bias towards majority classes and struggling to generalize effectively on minority classes. This limitation stems, in part, from the message passing process, leading GNNs to overfit to the limited neighborhood of annotated nodes from minority classes and impeding the propagation of discriminative information throughout the entire graph. In this paper, we introduce a novel Unified Graph Neural Network Learning (Uni-GNN) framework to tackle class-imbalanced node classification. The proposed framework seamlessly integrates both structural and semantic connectivity representations through semantic and structural node encoders. By combining these connectivity types, Uni-GNN extends the propagation of node embeddings beyond immediate neighbors, encompassing non-adjacent structural nodes and semantically similar nodes, enabling efficient diffusion of discriminative information throughout the graph. Moreover, to harness the potential of unlabeled nodes within the graph, we employ a balanced pseudo-label generation mechanism that augments the pool of available labeled nodes from minority classes in the training set. Experimental results underscore the superior performance of our proposed Uni-GNN framework compared to state-of-the-art class-imbalanced graph learning baselines across multiple benchmark datasets.