The ultrasound scanning robot operates in environments where frequent human-robot interactions occur. Most existing control methods for ultrasound scanning address only one specific interaction situation or implement hard switches between controllers for different situations, which compromises both safety and efficiency. In this paper, we propose a unified interaction control framework for ultrasound scanning robots capable of handling all common interactions, distinguishing both human-intended and unintended types, and adapting with appropriate compliance. Specifically, the robot suspends or modulates its ongoing main task if the interaction is intended, e.g., when the doctor grasps the robot to lead the end effector actively. Furthermore, it can identify unintended interactions and avoid potential collision in the null space beforehand. Even if that collision has happened, it can become compliant with the collision in the null space and try to reduce its impact on the main task (where the scan is ongoing) kinematically and dynamically. The multiple situations are integrated into a unified controller with a smooth transition to deal with the interactions by exhibiting human-intention-aware compliance. Experimental results validate the framework's ability to cope with all common interactions including intended intervention and unintended collision in a collaborative carotid artery ultrasound scanning task.