I have started a project just like this. I have a small picnic blanket that I was trying to duplicate but in a bigger size and make it look like a quilt on top. Picnic blankets have nylon on the bottom, which is much more managable and easier to wash than vinyl. The trick is to not have that much quilting on the bottom because as others have said, the wholes from the needle and thread going through will let water and dirt into the middle of the quilt. There are two ways to go about doing it:
If you want just a simple grid spaced quite large: Pick a pattern for the pieced top that will allow this. The last border of the quilt should be made with the nylon. Then add the batting (also have to find one that will allow minimal quilting) and use the nylon for the back. Quilt with a simple grid or something so that you won't have too many wholes in the back. Use the nylon for the border also.
If you want more quilting: Make any quilt top you want again using nylon for the last border. Then sandwich as usual using a thin batting and a basic muslin or something for the back (it will not show). Quilt everything however you want except the outside nylon border. Do not quilt that part. Then add a second bottom of the nylon. The first muslin bottom is only there to help quilt it. Now if you have a relatively small quilt, you simply add the border on and that is what holds it all together. That way there are no wholes (other than around the very edge) for water to get in. Yes the nylon is not quilted to it but if it is small then it won't really be a problem. I have seen many done like this. If it is a larger quilt (something more than lap quilt size), then re-quilt the whole thing (top, batting, muslin, nylon) but only with a basic grid or something and very very far apart, 1 -1.5 foot grid spacing is plenty. It works best to plan this out ahead of time so it doesn't look funny. You can quilt on top of quilt lines you already did or add more in. Whatever you want. And it doesn't even have to be a grid. It can be a few small stiches here and there just to hold the nylon to the bottom.
If you don't have too much quilting going through the nylon and you plan on using it on the ground mostly in grassy or dry areas then you can use it just like that. But if you really want to make sure it is waterproof you can spray the bottom with waterproofing stuff (can't think of what it is called at the moment). It is the same stuff you can spray on coats to make them waterproof. Places like Cabellas's or Sportsman's Wharehouse have it and I think Walmart too in the outdoor/camping area.
Hopefully that made sense. I have seen it done and it really works well. Good luck!