Sending an inflated Mylar balloon through the U.S. Mail in an approved box is legal in most cases--but may not be the most reliable way to send your good wishes across the country.
Mylar is a type of polyester with an aluminum coating of microscopic thickness. Air-filled Mylar is not restricted by the U.S. Postal Service.
Under U.S. Postal Service regulations, helium is a non-flammable, non-toxic gas classified as "Division 2.2." These materials may be sent through domestic U.S. mail (both surface mail and air mail), but not through international mail, according to the "U.S. Domestic Mail Manual."
Sending an inflated balloon via domestic air mail, though legal, may cause it to pop in the unpressurized cargo hold.
Local Air Pressure Differences
Sending an inflated balloon to a significantly higher altitude (e.g. from sea level to the Rocky Mountain region) may cause it to pop. Sending it to a lower altitude (e.g. from the Rocky Mountain region to sea level) may cause it to partially deflate.