S corporation has a problem in such a situation. In a C corporation, it (complete health insurance coverage) is allowed employee benefit deduction. In a non-profit organization, it should not be any problem. Health insurance coverage should be allowed. Most large companies and lawyer type of partnerships have complete health insurance coverage including even co-pays. That is, there is no deductibles and co-pays. Everything is covered by the employer as deductible employee benefit expenses.
In term of insurance plan, after the recent insurance policy change, all insurance policies need to cover basic essential care coverage. It should not matter. You want to take a look of the coverage. If the deductible is too low and the coverage is proportionally low, say 60% of 1M, then, you may want to get another high deductible health care policy as a co-insurance to protect your agency from the high risk possible for such a co-op church plan. There are co-insurance type, high deductible up to 20,000. Then, everything above 20,000, you are covered.
However, the non-profit organization needs to obtain the insurance policy for this employee. If any cash payment is made to the employee, that is, if the employee goes out to get the insurance policy him or herself, there could be a problem. Instead of an employee benefit of an insurance policy, it can become paying employees cash in different format. When I used to work for the IRS, I was told that it is fine for employer to pay directly to the insurance company. As long as the check is written to the insurance company, that is fine. But that was before the latest insurance policy change, employee insurance plan was relatively difficult to obtain. Nowadays, it is best to retain a group policy for this person directly by the employer.
Expense reimbursement should be limited to cell phone and mileages, etc. Any employee benefit allowed to other organizations, say C corporations, should be allowed to non-profits. S corporations have problems and much limitations because the law requires it to be the same as sole proprietorship, schedule C business. Then, almost most benefits are not allowed. Non-profit should be similar to C Corporation; it is an independent entity. All employee benefits should be allowed.
As an accounting professional, we need to be careful about the structural proportion between wage payment and employee benefits. But church has its own rules for paying wages and reporting income tax. I am just making a side note here. I know you know that.
Please feel free to follow up.