Role-oriented dialogue summarization aims at generating summaries for different roles in dialogue, e.g., user and agent. Interaction between different roles is vital for the task. Existing methods could not fully capture interaction patterns between roles when encoding dialogue, thus are prone to ignore the interaction-related key information. In this paper, we propose a contrastive learning based interaction-aware model for the role-oriented dialogue summarization namely CIAM. An interaction-aware contrastive objective is constructed to guide the encoded dialogue representation to learn role-level interaction. The representation is then used by the decoder to generate role-oriented summaries. The contrastive objective is trained jointly with the primary dialogue summarization task. Additionally, we innovatively utilize different decoder start tokens to control what kind of summary to generate, thus could generate different role-oriented summaries with a unified model. Experimental results show that our method achieves new state-of-the-art results on two public datasets. Extensive analyses further demonstrate that our method excels at capturing interaction information between different roles and producing informative summaries.