Is it possible to insulate a rolled comp roof from the outside?

I have a rolled composition roof that is similar to this on the outside...

http://farm4.static.flickr.com/3311/...d7abd62a95.jpg
and this on the inside...

http://images.vrbo.com/vrbo/images/2c8344

I love the look of the beamed ceiling so I don't want to put anything under it. The previous owner had put drop ceiling over it, but I took it down cause it was ugly. I stand by my decision, but that part of the house is an add-on and gets extremely hot and cold. I was wondering what I could put on top of the roof to insulate it better.

I know there's spray foam, but that gets expensive.

Could I roll out and staple that reflective insulation?

Any ideas?

 

commercial building use (generally) 2" thick poly-isocyanurate foam boards and generally apply an epdm (rubber) roofing material over that.

this type of board has an r value around 6.8 per inch

I do not know about laying it over the existing roof though.

 

If the existing roofing material is directly applied to the wood we see inside then yes, you can lay styrofoam directly on top of the old roof.
If there is an air space beneath the roof deck then no, you could trap moisture in the cavity if you insulated from above.

As a precaution and before doing anything with this consult a professional COMMERCIAL roofer who is experienced in flat roofing systems.