Randy's right. You explaining why you are denying the application, not why each person is denied. There is no privacy between joint applicants, when it comes to Reg B and reasons for denial. Saying "Joint Applicant's credit report" is also not a specific reason. You must provide a specific reason indicating why the credit report is not acceptable.
To address your second question about the FCRA disclosure, these may help you understand the requirements:
When there are two (or more) applicants, a creditor must provide an adverse action notice to both applicants if the application is denied, even in part, based on information in a co-applicant’s consumer report. [2011 FTC Staff Interpretations page 83] An applicant with strong credit who receives an adverse action notice will likely understand that the adverse action decision was based on the co-applicant’s credit information or will contact the creditor to inquire. [Federal Register/Vol. 76, No. 136/7-15-11/Rules and Regulations – Page 41596]
If credit scores are used, separate Adverse Action Notices should be provided to each applicant. Given privacy and customer relations concerns, the Board expects that creditors would generally provide separate FCRA adverse action notices to each applicant with only the individual’s credit score on each notice. The Board does not believe… that Congress intended for an individual to receive another individual’s credit score.. [Federal Register/Vol. 76, No. 136/7-15-11/Rules and Regulations – Pages 41596 and 41597]
Thus, the wife would get the FCRA Statement and FCRA Credit Score Information (If a score was used).