Well, I think there are two sides to Jamie's home birth. The side that really happened and at the side that we are seeing.
Most of the time when she is in the pool and screaming, we only see the back of the midwife or someone, not what Jamie is saying. So there is audio but who knows if it is really from that scene.
Also, I'm sure they filmed some scenes after everything was over, just for some "drama" scenes. We KNOW how this show is edited!