I can totally understand your husbands fear - my partner was similar.
His mother had a very 'negligent' doctor and she ended up tearing right through her rectum, they stopped counting at 150 stitches and now essenially has no function down there. She has a stoma (like a plastic poo bag) instead. Knowing this, he was very committed to "the knowledge of science" and would have much preferred me in private care.

But, his mum also used to work in medical records and advised things like this only happen in a very, very small percentage of births. And the way birth is handled these days is very, very different. The hardest thing for me was convincing DP to read and learn with me (so stubborn and hardheaded)! He would scoff at the power of breathing during birth (despite the fact it'sto do with supplying your uterus with more oxygen and therefor it working more effectively and lessening the pain). There is no harm in starting to look now for things that can help you during birth.

Learning about the best way to manage birth - the effects of induction, what an epidural does to slow down or hinder labour, ways to reduce the likeliehood of tearing, the causes etc. As they say knowledge is power.

ETA: What Tali said about the waiting for waiting period to be over before getting pregnant sounds right, as your birth would likely not be covered because your pre-exisiting condition; pregnancy was conceived before end waiting period.