Frontier has spent tens of millions of dollars to bring broadband to 158,000 additional households in West Virginia since 2010, the company has said.
Frontier would not comment on the House vote Tuesday.
The House bill also will allow the Broadband Deployment Council to distribute state grant money designed to encourage people to subscribe to broadband statewide.
Current law only permits the council to give "demand promotion" grants in remote areas that don't have high-speed Internet. Council members say it doesn't make sense to market broadband in areas where it's not available.
Some House Republicans said the money should be spent to upgrade broadband networks -- not to push people to sign up for Internet service.
"They say we need to be on the leading edge," said House Minority Leader Tim Armstead, R-Kanawha, who voted against the bill. "To me, promotion is not building infrastructure and improving access."
The bill next goes to the Senate.
Also Tuesday, House members:
* Approved a bill (HB3043) that would expand the state's mine safety tax credit to include methane monitors.
"I want the state to do everything possible to ensure that the most accurate safety equipment is in our coal mines," said House Speaker Rick Thompson, D-Wayne, who introduced the bill. "It is my hope that the expansion of this tax credit will encourage equipment manufacturers to produce the methane monitoring units our mining companies need in order to comply with our new, more rigid safety standards."
* Amended a bill (HB3157) that requires the state school board to look into ways to restore flexibility to county school boards. The amendment adds a provision that the state school board must also examine the increasing amount of reports and other paperwork principals and teachers must complete and submit to the state Department of Education. State lawmakers want the department to reduce school paperwork requirements.
* Passed legislation (HB2866) that allows gun owners to shoot weapons within 500 feet of their residence, provided there are no other homes located within the 500 feet.
Reach Eric Eyre at erice...@wvgazette.com or 304-348-4869.