Credit Unions are good at offering joint credit cards, the major issuers (Citi, Chase, BofA) not so much.
The aforementioned US Bank does offer joint (my former NWA Visa is a joint account). The current application page for their FlexPerks visa offers a joint option.
As to repairing credit, if one half of the equation has bad credit, a joint application can actually hurt. The weaker applicant can drag the whole application below the approval line. Better for the stronger party to sign up as a single and add the person with less than stellar credit as an authorized user.