He and Sarah, who stays home with their two toddlers, mail a flat $405 payment to a fellow member every month, the standard rate for families of three or more. Had they stuck with the insurance he was offered through work, the Doyles said, their share of the premium would have been about $600 a month, and they would have had to pay the first $5,000 in individual medical costs, $10,000 for the family, other than preventive care.

Under the ministry, they also have to pay the first $300 of any medical expense they incur. They have not yet had a doctor’s bill exceed that amount, though they are waiting somewhat nervously for that day to come. Samaritan limits spending on each injury or illness to $250,000, with exceptions for people who agree to pay extra each year toward others’ bills above that amount.

“There’s a little bit of fear going into it,” said Mrs. Doyle, 33, adding that she suspected she had a hernia that would need to be repaired soon. “What if people don’t pay their share and what if the money doesn’t come in? But that’s where the faith-based part comes in — I’m really going to rely on God.”

Mr. Lansberry said Samaritan members’ eligible medical bills averaged, cumulatively, over $16 million a month. Its membership has grown by about 50,000 over the last year, to nearly 200,000 people in 58,000 paying households.

Acknowledging that many families can qualify for subsidized insurance policies with free preventive care through the Affordable Care Act, Mr. Lansberry said that most new members were not “joining primarily on price; they are joining primarily on principle.”

Before members can be reimbursed, they sometimes must pay upfront for their medical care — potentially a sizable outlay, because hospitals increasingly require at least partial prepayment. It then takes at least two months for Samaritan to process their requests for help and for checks from other members to arrive in the mail.