If I am discharged for a joint debt, what happens to the cosigner?

Your cosigner's liability for the debt is not effected by your discharge.

Cosigners are almost always joint and severally liable. This means the creditor can collect the entire debt from any person who has signed for the debt. If one of the signers receives a discharge, the creditor will still be able to collect the entire debt (plus interest, attorneys fees and collection charges, if the contract provides) from the other signers.