But because median incomes have grown even slower during that same time, health insurance costs are eating up a bigger share of household incomes than ever, the Commonwealth Fund report found.
Given that fact, the report is titled, "The Slowdown in Employer Insurance Cost Growth: Why Many Workers Still Feel the Pinch."
Last year, the total amount of money a family paid on average for job-based insurance equaled 10.1 percent of median household income, the report said.
That compares to 8.4 percent of household income in 2010, the year the Affordable Care Act began taking effect — and to just 6.5 percent of income in 2006.
"As far as families are concerned, it's still hitting them," said David Radley, a co-author of Commonwealth Fund report, referring to the impact of health insurance costs.
"It doesn't, to an average family, feel like [insurance costs are] growing slowly," Radley said. "They're still facing a bigger burden than they did a few years ago."
The Commonwealth Fund report also gave a state-by-state breakdown of job-based insurance costs, finding that workers in Florida, Texas, Arizona, Mississippi and Oklahoma have the highest burdens.
In Mississippi, where income is low and health insurance contributions are high, families spent an average of 14.7 percent of their incomes on job-based health coverage. In the other four high-cost states, health insurance costs eat up 12 percent or more of median family incomes.
People with job-based insurance in Washington, D.C., and Massachusetts had the lowest costs on average, of 6.8 percent and 7.3 percent of median household incomes respectively, according to the report.
More than half of all Americans, 154 million people, get health coverage through either their own job or through a family member's employer.
That number dwarfs the 11 million or so people who get coverage through an individual market health plan sold through a government-run Obamacare marketplace.
The Commonwealth Fund report found a slowdown in the total costs of health insurance through an employer, and the share of those costs directly paid by workers. The report attributed that to a historic slowdown in the growth of the costs of health services.
The total premium paid for a health plan provided by an employer grew by an average annual rate of 4.7 percent from 2006 through 2010, the report found. But from 2010 through 2015 — the time span in which Obamacare has been in effect — that average annual rate slowed to 3.8 percent.
Total premium includes the share of monthly premiums paid for by an employer and the employee.
From 2006 until 2010, workers' share of the total premium grew an average of 6.7 percent annually. But from 2010 through 2015, that contribution grew by just 4.2 percent annually on average, according to the report.
The Commonwealth Fund also identified a slowdown in increases in the deductibles in employer-based plans since the ACA, but one that was less dramatic than the deceleration seen in premium inflation. Deductibles are the amount of money a person must directly pay for health-care services or medication before a plan covers its share of those costs.
From 2006 until 2010, deductibles grew by an average of 9.5 percent annually. Over the next half decade they grew by 8.5 percent, according to the report.