The measure also increases the size of property tax exemptions automatically offered to homeowners and senior citizens, but critics say the plan does little except make the property tax system more complicated and push more of the burden onto businesses.
The bill passed 77 to 39 and now goes to the Senate, which has approved similar legislation. The bill lets counties decide whether to adopt the three-year limits.
If they do, then each family's property tax bill would be calculated as if their home's value had gone up a maximum of seven-percent.
The bill also would give all homeowners a $5,000 tax exemption, up from $3,500 in most places. The senior exemption would jump to $3,000, up from $2,000.