Typically when I see this sort of behavior, it is because I haven't made sure that the two datasets are in the same coordinate system. If you have checked this, and are still experiencing issues, try exporting the vector data into a .dwg and the imagery into a stand alone file (e.g., a .tif or .jpg). To add the imagery, use the MAPIINSERT command.
Typically, I am working in some flavor of State Plane coordinates with a linear unit of US Survey Feet. When I export to CAD from ArcGIS Pro, Civil 3D does not recognize that the linear units are US Survey Feet and assumes International Feet. So, by default, I open the newly exported drawing and change the insertion units (UNITS command). For imagery, I have to open a new drawing, temporarily change the units to International Feet, use the MAPIINSERT command to add the image, then change the units back to US Survey Feet. When I do this, the imagery and linework line up with each other and survey data.
