Sketchup has a lot of cool ways to hone in on what you want to select. But if you want to select only the faces and no edges, I’m not seeing a way to do it other than selecting each face. My reason for this is that I want to be able to change colorings on large groups of faces using the Entity Info window. But if one or more edges is included in my selection, I can’t do it.
I read other forums where people suggested
Select the region, with the edges, then switch to wireframe mode and deselect all the edges in one swoop.
Turn off edges in the Styles window, then drag over the faces you want to select.
Neither of these things work. No matter what mode I’m in, dragging to select an area includes all the edges and all the faces that would normally be selected, whether they are visible or not.
Can’t see a way to do what you asked, but for times when you only need to change one side’s color it should work (in some cases you might have to reverse faces to see that it worked). Or for doing both sides could you not just do two paint bucket fills?