DOVER — Bob and Mary St. Germain say they can’t believe it. Four years after their son, Bryan, used his cellphone to connect to the Internet, the couple is still trying to fight the bill: a nearly $18,000 tab from Verizon.

Bryan, now 26, thought his family’s plan included free data downloads. It didn’t, and in August 2006, the St. Germains’ phone bill ballooned to more than 100 times the normal amount.

“You can’t print what my husband said’’ when the bill came, Mary St. Germain said. “He was very shocked.’’

Verizon eventually offered to reduce the bill by half, but Bob St. Germain, 66, a retired marketing professional, said he rejected the offer after consulting with state utility officials who advised him not to pay. So Verizon sent the reduced bill to a collection agency.

Verizon officials said that the charges were legitimate and that they have tried to work with St. Germain to resolve the dispute.

“We go to great lengths to educate our customers on their products and services so that they avoid any unintended bills,’’ Philip Santoro, a spokesman for Verizon Communications Inc., and Michael Murphy, a spokes man for Verizon Wireless, wrote in an e-mailed statement.

The case highlights how confusing wireless plans can be and how any misstep can be costly for customers. Sascha Meinrath, director of the New America Foundation, a nonpartisan research group in Washington, D.C., said cellphone contracts have become so bewildering that he fields at least one complaint a month from customers with sky-high bills looking for help. Meinrath said what outrages him is that many carriers offer unlimited data plans for about $30 a month and are “making money off that.’’

“So how is it that they were charging $12,000 a month?’’ he asked. “How is it conceivable that is not price gouging?’’

Kevin Brannelly, an official at the state Department of Public Utilities, tried to help the St. Germain family fight the bill because it did not seem right.

“Never in my 25 years here have I seen such stubborn and senseless resistance to what is obviously a mistake,’’ he wrote in an e-mail to St. Germain.

Telecommunications experts said it is difficult to know how much it actually costs Verizon to transmit data. Verizon and other wireless companies typically do not release that information.

Srinivasan Keshav, a professor of computer science at the University of Waterloo in Ontario, said the problem is not the cost of the service, but whether the customer knows the cost. He said customers are making mistakes because they do not have the time to sort through pages of fine print to understand the terms and conditions of a plan.