Debbie and Tab Bonidy of Avon filed their lawsuit last year, claiming the ban violates their Second Amendment rights, The Denver Post reported Monday.
Both have permits allowing them to carry concealed weapons and both say they carry handguns.
Because they don't receive mail at their remote home, they say the ban on guns in post offices and in their parking lots makes it impossible for them to get their mail.
James Manley, an attorney at the Mountain States Legal Foundation who represents the Bonidys and the National Association for Gun Rights in the suit, said the case could have nationwide implications.
"This is a situation that hasn't been challenged before, where you have members of the general public who want to exercise their right to carry," Manley said.
Senior U.S. District Judge Richard Matsch rejected a Postal Service motion seeking dismissal of the suit. The motion argued the ban is lawful and the Bonidys could park on the street and leave their guns in their car.
The Postal Service said the U.S. Supreme Court has affirmed an individual's rights to possess firearms but ruled they can be banned in "sensitive places."
"Large numbers of people from all walks of life gather on postal property every day. … The Postal Service is thus responsible for the protection of its employees and all the members of the public who enter postal property," the motion stated.