If both persons agreed to be liable for the account, which is likely the case if both are named on the bill, the bankruptcy of one will not result in a discharge of the other (the "co-debtor").
However, if the debtor files a chapter 13 petition, the co-debtor stay will prevent collection from the co-debtor (at least temporarily) to give the bankruptcy debtor the opportunity to pay. The co-debtor can be pursured eventually if the debt is not paid in full.
