First of all, I am not a coach. I started learning butterfly stroke following the video "Better Fly for Every Body" a year ago. And now, I can swim this stroke 100 meters. The first 75 meters are in good shape, but the last 25 meters is kind of tired and short of breath. I understand I still have a long way to go.
As you said the breathing-in starts when your mouth is clear and out of water. Attached are some still images I found in YouTube. They are about the positions between hands and head. Hope they are helpful to you.