With three part-time jobs, a 14-month-old son with Down syndrome and two other children with autism, Lisa Carey has plenty to keep her busy.

So when the Los Angeles mother began receiving bills last year from her health insurance company asking her to pay more than she believed the policy called for, it was a hassle she could do without.

The 41-year-old had purchased a family health insurance plan from Anthem Blue Cross with an annual out-of-pocket maximum of $13,000. Once the out-of-pocket medical expenses for two members of her family reached that amount, Anthem was supposed to pay all of her family’s covered health costs for the remainder of the year, said Carey, who lives in the city’s West Hills neighborhood. Out-of-pocket expenses include co-pays, deductibles and other costs that policyholders must pay before their plan begins picking up the full tab for covered benefits.

Under the Affordable Care Act, the maximum out-of-pocket cost in 2014 is $6,350 for an individual and $12,700 for a family, excluding some grandfathered plans with higher maximums. The new law, known as Obamacare, is designed to help reduce out-of-pocket expenses.

But California advocates say the law doesn’t go far enough, because it doesn’t require insurance companies to notify policyholders when they’ve reached their maximums, sometimes leading them to go on paying bills they don’t actually owe.

“It’s very common,” said Karen Fessel, founder and executive director of the Autism Health Insurance Project, a California group that’s trying to change insurance billing practices. “It has to do with autism just in that our kids use a lot of services, but it affects anyone that uses a lot of services. If you have cancer in a given year, you’re going to burn through that out-of-pocket annual maximum.”

“There’s loads and loads and loads of people who are impacted by this.”

With the birth of her son and the expensive medical treatment he required as a newborn in early 2013, Carey’s family hit its out-of-pocket maximum in March last year. Yet each time Anthem processed a claim, the company failed to take that into account, continuing to charge her for expenses that should have been fully covered, she said.

“Every single claim that came in I had to call them and say, ‘I’ve met my out of pocket maximum, you need to reprocess this,’” Carey said. “They said that they would do something in their system so I would stop having to call.”

But despite continued assurances from Anthem, the problem never got fixed, Carey said. Instead, she would spend hours on the phone each week trying to get her claims reprocessed, time she would have much rather spent working or taking care of her children.

Carey’s experience is far from unique, according to the Autism Health Insurance Project. The organization checks health-plan statements for families who are struggling to make sense of their medical bills and has found that insurance companies frequently charge policyholders for medical expenses after they’ve reached their out-of-pocket maximums, Fessel said.

The result is that families often end up paying more for their health care than they should under the terms of their insurance plan, she said.

The Autism Health Insurance Project is working with state Senate President Pro Tem Darrell Steinberg, D-Sacramento, on legislation to change this situation. A Senate bill introduced by Steinberg in February would require private insurers to keep track of out-of-pocket expenses and notify policyholders when they reach the maximum under their plan.

Steinberg hopes the Legislature will pass the bill by September so it can go into effect next year, his spokesman Rhys Williams said.

In the meantime, trying to get insurance companies to pick up the tab for medical expenses once the out-of-pocket maximum has been met is often a long and arduous process, Fessel said. She and many of the families her organization works with have routinely found they must call companies multiple times to get claims corrected.

The problem appears to happen with all health insurance providers, Fessel said, but some make the correction process more difficult by requiring customers to submit receipts as proof they’ve met their out-of-pocket expenses.

The result is additional stress — not to mention financial strain — on families already struggling to cope with challenging health conditions, she said.

The families “have to basically be on top of it in order to get money reimbursed,” Fessel said. “The onus is on them to take responsibility for it, and these are families that are dealing with children that are very, very difficult to work with and so a lot of their energy is going into making sure their children get the treatments that they need, so they can’t be keeping up on all the payments.”

Ashley Greco of Pleasanton can relate to that. Greco’s four-year-old son has autism, which requires him to undergo 35 to 40 hours of therapy each week.

Last year, her family reached its out-of-pocket maximum of $6,000 under their plan with Blue Shield of California, she said. But the family kept receiving incorrect bills — sometimes for thousands of dollars — from the company and a behavioral-health administrator it contracts with, Greco said.

It was only after months of phone calls to the company and administrator, and the intervention of a human resources specialist from her husband’s employer that Greco said she was able to get the issue partially resolved.

“Dealing with making sure that my child has everything that he needs on top of dealing with the insurance companies that are not properly following our plan was just extremely stressful,” she said.

Blue Shield of California did not reply to requests for comment before this article’s deadline.

A spokesman for Anthem said the company could not speak specifically about Carey’s case for confidentiality reasons and referred general inquiries on the issue to the California Association of Health Plans, an advocacy group for the private health insurance industry.

Kaiser Permanente, the largest provider of private health insurance in the state, replied to requests for comment with a statement saying members can track expenses that count toward their out-of-pocket maximums themselves through an array of customer service options.

Nicole Evans, a spokeswoman for the California Association of Health Plans, said she was not aware of any widespread problem related to health companies not tracking out-of-pocket maximums. She said it’s possible that sometimes insurers don’t have up-to-date information on how much members have paid in co-pays toward their out-of-pocket maximums because the companies are still waiting to receive that data from a provider.

“Hopefully (the policyholders are) working with the plans and contacting them because that’s something I think the plan would want to make sure they’re addressing on behalf of their membership,” Evans said.