If you mean the vertical risers in a raceway within the building, see 300.19(A).
If you mean is THHN permitted for outdoor service installations, the answer is no, THHN is not permitted in outdoor/wet locations.
Most conductors being manufactured today have dual insulation values, such as THHN/THWN. Those conductors are permitted to be used outdoors and in exposed situations such as at the weatherhead.
UL White Book
THERMOPLASTIC-INSULATED WIRE (ZLGR)
PRODUCT MARKINGS
Types TW, THW, THW-2, THHW, THWN, and THWN-2 in all sizes tha are marked "Sunlight Resistant" comply with an artificial weather test.
This means they can be installed outdoors, in sunlight.
See also
310.8(D) Locations Exposed to direct Sunlight.
What the local POCO determines is a different issue and applies to that jurisdiction.