The rapid advancement of conversational search systems revolutionizes how information is accessed by enabling the multi-turn interaction between the user and the system. Existing conversational search systems are usually built with two different models. This separation restricts the system from leveraging the intrinsic knowledge of the models simultaneously, which cannot ensure the effectiveness of retrieval benefiting the generation. The existing studies for developing unified models cannot fully address the aspects of understanding conversational context, managing retrieval independently, and generating responses. In this paper, we explore how to unify dense retrieval and response generation for large language models in conversation. We conduct joint fine-tuning with different objectives and design two mechanisms to reduce the inconsistency risks while mitigating data discrepancy. The evaluations on five conversational search datasets demonstrate that our unified model can mutually improve both tasks and outperform the existing baselines.