Test any stabilizer on a scrap piece of Jersey first. Some of them will stiffen the hand too much. Nylon tricot iron-on interfacing is what I have used for silks; it has a soft hand.
Also, I'm wondering if Jersey will melt under a hot iron, making an iron-on stabilizer inadvisable. If it does, you might want to experiment with heavy starching instead. Mix a 1:1 solution of Sta-Flo liquid laundry starch and water, brush it on until the fabric is saturated, then dry on a line. Should require minimal ironing to get creases out. This might stiffen the jersey enough to cut and sew without ironing on a stabilizer.
If neither of the above works, you might have to do paper foundation piecing or iron on freezer paper. (Freezer paper does not require as much heat as iron-on interfacing.)
With any of these techniques, make the pieces as large as possible so you don't drive yourself crazy.