Hi Leslie,
I've done it many times. The instructions originally came from Judy Turner's "Awash With Color" Quilt-As-You-Go (QAYG) book ( btw, a FABULOUS book). I don't have the book handy so I can't look up the exact directions.
Try this will some scraps first.
As I remember it - you cut one color 7/8" (brown) and the other color 1 3/4" (navy) . Sew them together with a regular quarter inch seam. I used a smaller stitch length because the seam line will eventually land on the edge of the quilt. Fold the binding strips in half as you normally would. Attach it to the quilt with the brown binding right sides together with the brown side of the quilt.* Now wrap it around to the other side and you should see navy binding . Sew it down however you normally would.
I do believe there is always going to be a hair of the other color binding showing on the one side but that's how you do it. Also, for some strange reason, the miters work out perfectly. I was kind of astounded the first time I did it.
- I can't remember if you first sew down the smaller or larger colored binding...I vaguely remember something about sewing the binding to the back and bringing it around to the front..I guess it depends on which side you want to sewdown by hand (?).
Again, keep in mind I'm writing this from memory with no fabric in front of me. I'm playing with Post-Its. I think those measurements are correct for a finished 1/4" binding. Try it with 3" long scraps first. Somewhere, in the mess of my sewing room, I have a sample with the directions pinned to it. It comes in handy. When I'm actually in the sewing room. And I can find the sample.
Also, Sharon Pederson had a different method in her book (Reversible Quilts). It was more like single binding and I didn't think it was as strong. I used the above method on numerous QAYG baby/kids quilts, and the bindings are still in great shape years and tons of washings later. I doubt your quilt recipient is going to be as hard on your quilt as these kids were on theirs.
You didn't post a picture of the quilt tops, but would a stripe like this work on both sides (if you didn't want to go the 2 sided route):
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Hope that wasn't too confusing. If I can find the book, I'll correct any errors.
-Michele in NYC