When I deselect everything in the 3D viewport, everything in the image editor disappears. When I select any portion of the mesh object, only the unwrap for that selected portion is displayed. How do I fix this?
Check to make sure you don't have selection syncing enabled between the 3D View and UV Image Editor. It's the button called "Keep UV and edit mode mesh selection in sync". The icon is a mouse cursor over a cube and 2 verts.