If you can't ping across the link as well, it's possible the LEC's switch is falsly reporting the circuit as up. Or, it's possible there is a LMI mis-match between you, telco or your provider.

IMO, the best way to make use of both links is to load-balance them using BGP. This, of course, assuming both E0 and S0 terminate on different aggregate devices.

A simple way to explain it is the same way you would with the 'show frame-relay lmi' for a f/r connection.