You can use the "backup interface eth1" under the serial interface to use eth interface as a backup of serial for a route to internet..
Also you can use two static routes, one with lower metric pointing to serial interface and one with higher metric pointing to eth1 interface..
So the moment serial interface went down, the static route thru it will be purged from the routing table and other route will be used...
Here is a verygood link which discuss "how to determone which backup scheme is good for your network"
http://www.cisco.com/warp/public/123/backup-main.html
thanks..Tejal