The Shiela book is absolutely the right start!
I've pulled rank on my DP and told him that as I will be the one giving birth, I want to do it the way I feel fundamentally inclined, and that's a HB. He KNOWS all about the risks of hospitals, and even birth centres attached to them (like our local FBC - it is still governed by policy, even if it is a far better policy than the maternity ward). It's the money factor with my DP, not the safety aspect - he's pretty clued up in that respect.
Now, if you can get your hands on it, get him to watch with you The Business of Being Born...that's gotta be compelling for anyone who needed convincing!
Yours isn't the first to baulk at the idea of HB, and I'm sure he won't be the last to be converted
Good luck!