The behaviour is normal.
Consider that in display textured mode you'll see the last selected texture in the UV/Image editor for the selected faces... so it may not be one of the material's texture. There's no correlation between the material texture and the textures shown in the textured mode of the 3d view, unless you keep it consciusly. So keep an eye on it...
I could not find two of you textures (Texture.png and Texture.png.001 are their names) so I have replaced them with my own creation: Untitled (all right reserved...!!!)
We have a single object with two material and two UVMap.
The second UVMap is "empty", ... well not really,.. let's say it not contains useful info as is collapsed. Remove it by selecting it and pressing the minus.
Now we have a single uv map, but as contain the info for both material, it shows them overlayed.
1) Select all the faces of one material (Edit mode, deselect all, material tab->Select) and hide them:
2) Duplicate the uvmap, rename, make active first UVmap, select first material faces, invert selection, make uv info related to these faces unobtrusive in the uv/image editor (move them away, or scale them to a 0 factor..). Than select second UVmap, second material faces....and repeat as above.
By selecting one of the UVMaps with one clock you are now able to see only the its relative UVinfo.
(Note: remember to update Image mapping coordinates in the material's texture, they must point to the correct UVMap)
In both methods you are not allowed to see the texture of the other material while UV editing one
3) Assuming that you have one map with UVs overlayed, you can:
- Unselect all
- Go to the material tab and select one material's face
- Go to the UV/Image editor, select all visible
- Set repeating coordinates
- Shift your selection on the x-axis by the texturex with (in pixel)
- Select all in the 3d view
Nothing should have changed, as the texture UV are repeated by default (if no clamp option by enabled), but now you can clearly see and edit both UV layouts
(Note: not shure what to do if the X size is different between textures..)
4) As suggested by gladys, split the objects in two and merge the parts only at the end is the fastest solution.