In the field of high-end equipment assembly, an increasing number of products cannot be assembled solely by humans or machines alone, which shows the assembly process emphasizes efficient human-robot collaboration. Robots and human share the same workspace, with robots handling repetitive or hazardous tasks through safe interaction, while humans oversee decision-making and control. To further improve assembly efficiency and applicability in complex production environment, this paper proposes a multi-agent and industrial language model framework for Human-Robot Collaborative (HRC) assembly. A Multi-Agent System (MAS) enhanced by Large Language Model (LLM) is established both for human and robots to achieve the assembly process interaction, which perform the HRC execution relative to assembly tasks. Besides, Digital Twin (DT) technology enhanced by Vision Language Model (VLM) is leveraged to collect real-time status data and cognize collaborative assembly environment, which perform the assembly execution and decision-making under the enabling of the MAS. Then, A HRC assembly mechanism that makes the real-time dynamic assembly decisions is brought to make the assembly process intelligent enough to address the influences of different degrees of exception. Based on the human-robot orchestration established above, the HRC assembly task planning model is presented to support the global optimal configuration of the assembly resources by combing Knowledge Graph (KG) and industrial language model (ILM), which reflects the actual assembly scenario of the HRC process. In addition, a decision prediction model driven by holistic empirical data and ILM for local assembly adjustment is also developed, which reveals that the ILM can capture the underlying logic of complex human-robot collaborative assembly process and provide optimization solutions. Finally, the efficiency and applicability of the proposed framework are verified through a design case.