Take your placket pieces and fold one of the long edges in 1/2 inch. Press this well. Place your strip of fusible interfacing on the placket piece and make sure that it is at least 1/2 inch from the other edges. Fuse it in place.
Now, Lay the placket piece down right sides together on the front of the jacket. It will hang off the top and bottom by 1/2". Stitch the seam and press it open. Like so....
Fold the placket in half, right sides together, The creased edge will meet the seam that you just made.
Sew along the top and bottom edges of the placket, using 1/2" seam allowance. Turn it right side out, and press. I clip my corners before I press because I find that it has a crisper look to it. Position the placket fabric so that the edge that is in the inside of the jacket covers the seam that is there and top stitch it together.