My suspicision is that the points are not in the same coordinate system as the imagery. Particularly if you use the Add XY tool in ArcMap, it will default to assigning the data frame's coordinate system to the XY data. If the XY data is not already in that coordinate system, you can get the problem you listed with not being able to view all layers at once. When a coordinate system is assigned as in the Add XY tool, Define Projection tool, or data's property page in ArcCatalog, it updates the metadata only, the coordinate values are not changed. You have to assign the coordinate system that the data is in, then use the Project Tool or let ArcMap project the data on-the-fly to put it into a different coordinate system.
If the imagery is in a projected coordinate system, I think the points are lat/lon, a geographic coordinate system.
Melita