Learning effective representations is imperative for comprehending proteins and deciphering their biological functions. Recent strides in language models and graph neural networks have empowered protein models to harness primary or tertiary structure information for representation learning. Nevertheless, the absence of practical methodologies to appropriately model intricate inter-dependencies between protein sequences and structures has resulted in embeddings that exhibit low performance on tasks such as protein function prediction. In this study, we introduce CoupleNet, a novel framework designed to interlink protein sequences and structures to derive informative protein representations. CoupleNet integrates multiple levels and scales of features in proteins, encompassing residue identities and positions for sequences, as well as geometric representations for tertiary structures from both local and global perspectives. A two-type dynamic graph is constructed to capture adjacent and distant sequential features and structural geometries, achieving completeness at the amino acid and backbone levels. Additionally, convolutions are executed on nodes and edges simultaneously to generate comprehensive protein embeddings. Experimental results on benchmark datasets showcase that CoupleNet outperforms state-of-the-art methods, exhibiting particularly superior performance in low-sequence similarities scenarios, adeptly identifying infrequently encountered functions and effectively capturing remote homology relationships in proteins.