If that wasn't painful enough, deductibles—or the amount a person has to pay out of pocket before an insurance plans covers medical costs—more than doubled over the 10-year span.

Read MoreOne 'buck' a day for keeping the MD away



And despite a recent slowdown in costs that coincided with the adoption of the Obamcare health-care reform law in 2010, the price of job-based coverage is still rising faster than incomes, according to the report.

Families are "being squeezed by health-care costs," said report co-author Sara Collins, vice president for Health-Care Coverage and Access at the Commonwealth Fund. "Growth in family income is so slow that people still feel a pinch from health costs."

Job-based health insurance is, by far, the single biggest form of health coverage in the United States. Some 153 million people, or 57 percent of the population, are covered by health plans offered by their employer, or the employer of their spouse or parents, while the biggest provider is government-run Medicaid, which covers about 50 million poor adults and children.

From 2003 to 2013, the average premium for an individual worker covered by a job-based plan rose from $3,481 per year to $5,571 per year—a 60 percent increase.

Family coverage, which grew by 73 percent, went from an average of $9,249 in 2013 up to $16,029 in 2013, according to the Commonwealth Fund.

Because of the relatively slow growth in wages at the same time, total average premiums paid for a family getting coverage through a job went from being 15 percent of median income in 2003 to 23 percent in 2013.

Read MoreVaccination laggards vex parents



The bulk of the premiums for job-based health insurance is still paid by employers, as opposed to the employees covered by plans.

But since 2003, employees have had to shoulder a bigger share of those premiums, and a significantly large out-of-pocket costs, specifically deductibles, as employers sought ways to control their health-care costs. And more workers are covered by plans that have deductibles now than did a decade ago.