On the knit pieces, use a stabilizer meant for knits. After many failures with the Pellon-types, the best ones I found for general sewing with knits are Fusi-knit and French Fuse, which are both virtually the same-- a fusible tricot knit. Read the directions carefully so that you fully fuse the interfacing without scorching. It is usually available at my local Hancock's, but can also be found online. This product is very lightweight, but it does a great job of stabilizing without stiffness or bubbling.