You mean that black felt like stuff ?
Any type of digger, including mice, would go through it like it wasn't there.
You can bury welded wire.
or
Try finding the used chain link that is galvanized & plastic coated. I have 9ga galvanized chain link buried and expect it to out last me :
http://www.thatquailplace.com/smf/index.php?topic=4167.15