I am in the process of making a reversible quilt. I got the idea from this video.
http://www.youtube.com/watch?v=8bSGZbxfekw
I can't understand the language, but the video is so excellent, and it's easy to understand.
I am making it to use up strips, but in actual fact, I see no reason why you couldn't quilt a square made with solid fabrics, cut, flip one and join them into a Drunkard's path type of quilt. Using the bias fabric makes it so easy to do the curves, and I see no problems in joining the blocks.