Ok mate,

green as grass BUT I converted to sub-d (ie ~ button) then went to modify>convert>sub's to poly> and changed it to adaptive. This hasnt completely cleared it AND you have a higher poly count but I honestly cant see a better way. Unless you leave them as seperate mesh?? That is a hard one

cheers bullet

btw I didnt add any more lines than you had apart from the extruded box.

EDIT: sorry, I duplicated the faces, moved, extruded for thickness. Then extruded again to the centre, then boolean to get that result. Mucked around with split poly etc, hope I havent made a numbnuts of myself. I think I also made the faces bigger than the original so the edges ended up between vert loops.