The average total cost of employer-provided health coverage passed $20,000 for a family plan this year, according to a new survey, a landmark that will likely resonate politically as health care has become an early focus of the presidential campaign.

Annual premiums rose 5% to hit $20,576 for an employer-provided family plan in 2019, according to the yearly poll of employers by the nonprofit Kaiser Family Foundation. On average, employers bore 71% of that cost, while employees paid the rest.

“It’s...