They do have a measure that also reflects underemployment. The broadest measure is called U-6, "Total unemployed, plus all persons marginally attached to the labor force, plus total employed part time for economic reasons, as a percent of the civilian labor force plus all persons marginally attached to the labor force." That also include the U-5, "discouraged workers, a subset of the marginally attached, have given a job-market related reason for not currently looking for work."

The measures are available, and they're usually in the vicinity of twice the regularly-reported (U-3) rate.

https://www.bls.gov/news.release/empsit.t15.htm