Per their website...
The command provides assistance to a Primary Agency when tasked by DOD. Per the Posse Comitatus Act, military forces can provide civil support, but cannot become directly involved in law enforcement.
USNORTHCOM was called up in 2003 for the Space Shuttle Columbia disaster. They were also called up in 2005 for Hurricane Katrina disaster relief, in this case they used the local public safety trunked radio system. In 2007, USNORTHCOM was requested to send US Navy dive teams to the Minneapolis/St.Paul area when the I-35 bridge crossing the Mississippi River collapsed during rush hour. Also in 2007, USNORTHCOM provided assistance to firefighters here in Southern California during a rash of wildfires by providing MAFFS and Federal Fire support.
Frequencies will vary greatly depending on the units located near you, if any. Voice traffic is rare depending on the type of incident or exercise they are involved in and where it is located. USNORTHCOM recently participated in an urban assault exercise here in Los Angeles with the LAPD. The copters went in blacked out and troops rappelled onto the roof of the US Bank building. No comms were observed during the week long exercise, not even air to air traffic. During disaster relief exercises you may hear some voice traffic but the bulk of their radio traffic is ALE nets and FEMA/SHARES events.