John Andrisan has modified this model so it is the same color on both wings. What he does is make the piece of paper 1 x 2 (tear a square in half) and fold it (back into a square) so there is colored paper on both sides. John says the extra thickness makes no difference. Alternatively, paper the same color on both sides could be used, e.g. colored bond paper cut into a square.
Regarding flatness, apparently Boaz bends the butterfly a little so it looks a bit three-dimensional. John's version, on the other hand, is flat. So the butterfly can be made either flat or three-dimensional.
Additional note: Kim's Crane has a wide range of square origami paper with both sides the same color. The way to find ordinary two-sided same-color paper is: go to http://origamipapersandbooks.com/ then type into the "quick find" box the following code: ac11y. She also has washi the same on both sides. It is difficult to find at the website, so write to me and I will send you the links.
Another note: Apparently the museum is happy to have origami butterflies, three dimensional or not!