Just off the top of my head i know there is the New Jersey roadset which is available in a shapefile and it has linear referencing, it is available @ http://www.state.nj.us/transportation/gis/data.shtm it states:
"The NJ Roadway Network file is the Official LRS for the New Jersey Department of Transportation. The file is a geodatabase that includes a linear referencing system that represents the public roadways in New Jersey. It was developed for use with ESRI’s geographic information systems applications and was structured to conform to the UNETRANS data model. The NJDOT data model reflects some of the key components of the UNETRANS model as outlined in the Transportation Data Models Analysis Report (pdf 2.5m).
The “NJ Roadway Network” is updated every calendar year. The database contains over 39,000 miles of roadway which includes Interstates, Toll routes, US routes, State routes, County routes, Local streets and Ramps.
For additional information on the “NJ Roadway Network”, refer to the metadata that is included with the file."
also see maybe:
https://gis.utah.gov/data/sgid-transportation/roads-system/ << down the page under highway linear referencing