Yes, its perfectly compliant to run a AL feeder to a sub panel. You cannot use AL for branch circuits rated at 15, 20 and 30 amp. I doubt its even made anymore.
You will not see the URD listed in the NEC either. But will see several AL wire types listed for use. You will need to see whats on the jacket of the URD, but in most cases it is listed.
URD is just a term. Not really a listed wire type.
The stuff at Lowes and HD are listed for the purpose. Be careful as some cannot enter the structure or dwelling. Be sure it can unless you put a disco outside and enter the building with copper or listed AL.