Many consumers with insurance are forced to pay hundreds and even thousands of dollars a year on mental-health care despite a 15-year-old law that is supposed to make such treatment as affordable and accessible as any other type of medical care.

Now the Biden administration wants to impose new requirements on insurers that it says would reduce out-of-pocket costs for mental-health care and substance-use-disorder treatment. The insurance industry is firing back, arguing the proposal would drive up prices and set impossible-to-meet standards.