I think Patrick did mention the possibility of binding the seams, but I can't quite remember the context.
If I wanted to make a reversible jacket (or just one with a very neat inside) I would do something similar to quilt-as-you-go. Having pieced, sandwiched and quilted* I would sew the seams through one layer and the wadding, and then oversew the other side.
* Quilting would need to be kept a little over two seam widths away from the edge to make this possible.