How about interlining them? You can buy a thick fluffy fabric called Domett in different weights/thicknesses which you sandwich between the face fabric and ordinary lining. If you cut it to the finished
size of your blind you can then wrap the face fabric over the edge of it (you would need to hand stitch the turning to the interlining using something like a herringbone or loose hemming stitch) before attaching the lining by hand hemming around the edge. This way the domett lies between the face fabric and all the other layers, so it should conceal all the turnings etc even with the light shining through. If you stab stitch through the blind every few inches along the rod pockets this will hold the layers together. You can buy the domett at:
They will supply samples if you want to see which weight would be suitable.
Bear in mind that if the blinds are large they will be quite heavy with interlining added, and you may need also to use extra rows of interlocking stitches to hold it to the face fabric. The domett is a bit of a pain to work with as it sheds fluff everwhere (and makes me sneeze!) but it does give a very luxurious look to the finished product.