Evaluation metrics shine the light on the best models and thus strongly influence the research directions, such as the recently developed dialogue metrics USR, FED, and GRADE. However, most current metrics evaluate the dialogue data as isolated and static because they only focus on a single quality or several qualities. To mitigate the problem, this paper proposes an interpretable, multi-faceted, and controllable framework IM^2 (Interpretable and Multi-category Integrated Metric) to combine a large number of metrics which are good at measuring different qualities. The IM^2 framework first divides current popular dialogue qualities into different categories and then applies or proposes dialogue metrics to measure the qualities within each category and finally generates an overall IM^2 score. An initial version of IM^2 was submitted to the AAAI 2022 Track5.1@DSTC10 challenge and took the 2^nd place on both of the development and test leaderboard. After the competition, we develop more metrics and improve the performance of our model. We compare IM^2 with other 13 current dialogue metrics and experimental results show that IM^2 correlates more strongly with human judgments than any of them on each evaluated dataset.