I don't know about health insurance in particular, but I am the third generation that I know of in my family to have insurance policies through the Greek Catholic Union, which has been around for this purpose since 1892.

There's also plainly church-based healthcare. Members of Amish churches believe they should take care of each other, so money is pooled and if a family cannot cover medical bills themselves, the church pays the rest. They also negotiate discounted rates like a health insurance company would. I know this isn't an academic source, and I can't remember where I heard about this before (ex-Amish blog? the Plain Reader? documentary?) but this explains why the Amish are exempt from the ACA due to already having it covered internally: http://www.phillymag.com/news/2013/10/09/amish-get-opt-obamacare/