In recent years, there has been an increasing number of frameworks developed for biomedical entity and relation extraction. These research efforts target the accelerating growth in biomedical publications and the intricate nature of biomedical texts, primarily written for domain experts. To handle these challenges while ensuring efficient knowledge utilization, we propose a novel framework leveraging both external knowledge bases and pre-trained biomedical language models. The design of our model is inspired by how humans learn advanced, domain-specific subjects. In particular, humans usually start by acquiring the most basic and common information to build a foundational understanding of a field. They then use that as a basis to extend to various specialized topics. Our approach employs such common-knowledge-sharing mechanism to create a task-independent and reusable background knowledge graph for biomedical entity and relation extraction. Notably, the graph allows easy transferability across biomedical texts from different domains. We demonstrate competitive results on key benchmarking tasks, including biomolecule binding interactions (BioRelEx) and adverse drug effect identification (ADE).