More than one million Americans have joined Christian groups in which they agree to share their medical expenses with other members. People are attracted by prices that are far lower than the cost of traditional insurance policies, which must meet strict requirements set by the Affordable Care Act, like guaranteed coverage for pre-existing conditions.

The Christian groups can offer low rates because they are not classified as insurance, and are under no legal obligation to pay medical claims. Some people have paid hundreds of dollars a month, and then have been left with hundreds of thousands in unpaid medical bills in several states where the ministries, which are not subject to regulation as insurers, failed to follow through on pooling members’ expenses.

With millions of Americans now without health insurance because they lost their jobs, critics of these plans worry they will turn to these alternatives without realizing they do not provide adequate protection.

In the current environment, “people will be desperate for health coverage, and they might sign up for things that look at first blush like a cheap deal,” said Eleanor Hamburger whose firm, Sirianni Youtz Spoonemore Hamburger, brought the three lawsuits and is seeking class-action status for them.

“We’ve fielded calls about Aliera from all over the country,” she said.

In an interview, George T. Kelly III, the Missouri man bringing the suit against Trinity and Aliera, said he and his wife were looking for plans when an insurance agent told them he “had a good deal for us.” In 2018, he signed up for the plan and paid “contributions” of $344 a month. But he discovered that the plan would not pay for any of his medical claims, including hernia surgery.

“They were just denying it,” he said. Mr. Kelly eventually went to an out-of-state surgery center where he could pay cash.

Jay Angoff, a former federal health official and state insurance regulator who is one of the lawyers representing Mr. Kelly, said people are being misled by Aliera and Trinity. “On the one hand, they state, sometimes in small print, that they’re not insurance,” he said. “On the other hand, they convey the impression they are insurance.”