you can still slip your lining inside the outter jacket like you planned, line up sleeves, edges. and just do some quilting before adding the binding around the edges. some straight stitching in the ditch here and there should be sufficient. check the package of batting you are using and see how close it should be quilted and follow that guideline then bind as planned. wash it gently in cold water for the first time...dry on low heat. press it and it will be beautiful!
i did this once...and one side was homespuns/flannels...i was really in a panic...but it turned out just fine, i had no problem with noticable distortion or shrinking unevenly. and i did not do a heavy quilting...i just followed the batting requirements (mine was quilt every 4") but different batts require different distances, so check yours.
it will turn out just fine...