It sounds to me like your machine tension might not be even or the fabric is somehow getting pulled tight as you sew it. If the outer fabric is getting pulled, or if it’s being push along with the presser foot as you sew, that would result in a curling edge. Maybe try reducing the amount of pressure your presser foot is putting on your fabric (if you can) or check your tension to be sure it’s balanced.
With regard to your interfacing, here are a few suggestions:
Try handwashing it in warm water (line dry) before using to prevent shrinkage.
Also: press, don’t iron. In other words, press the interfacing straight down (the weight of your iron is enough pressure) using some steam. Then lift your iron before putting it back down. Don’t slide the iron or it might stretch/shift the interfacing to cause bubbling. Once it’s applied you shouldn’t have problems with it. If you do, you might want to try a different brand/quality.
I hope that helps!