When Ray White’s son was about 9 years old, he struck a tree branch while riding his bike. Within minutes, an ambulance whisked him off to the emergency room. The boy recovered, but many months and phone calls later, Mr. White’s insurance company still had not paid the $200 ambulance bill, even though the insurer had assured him it was covered. He finally decided it was easier to pay it himself.

But by then, it was already too late. Unbeknown to Mr. White, the debt had been reported to the credit bureaus. It was only when he and his wife went to refinance the $240,000 mortgage on their home in Lewisville, Tex., last month — nearly six years after the accident — that he learned the bill had shaved about 100 points from his credit score. Even with no other debts, a healthy income and otherwise pristine credit, the couple had to pay an extra $4,000 to secure a lower interest rate.

“It wasn’t like I ignored it,” said Mr. White, 47, an executive in Internet advertising. “It’s not like I’m a credit risk in any way, shape or form.”

Even people with good insurance coverage know how hard it can be to figure out how much they owe after a visit to the doctor or, even worse, the emergency room, which can generate multiple bills. But as patients become responsible for a growing share of costs — not just co-payments, but also deductibles and coinsurance — bill paying is becoming ever more complex.