Insurance around the world confuses me too.
Here in Australia we have Private Health Insurance, which you decide whether or not you pay into. If you don't by age 30, you get taxed more. You can have different levels of cover for different things. We have the Top Hospital cover and Top Extras (extras like Chiropractor etc) and when it comes to pregnancy, you are covered for everything in the hospital, so it's super lovely as you have your own room, often double bed, really nice food etc and my hospital offers you (all being well) to be transferred to a suite at the Park Hyatt Hotel for 2 nights, which is just devine! However, to have the private hospital and everything, you have to have a private Obstetrician and you get no rebate through private health insurance for consultations or the scans and things that you go for. You do get Medicare rebates, which for example, my 13 week scan will be $220, and I'll get about $57 of that rebated. So it's something, but still lots extra even if you've already paid into your insurance.