Below Query shall return the mappings for the requested DbName

    SELECT 'DbName', dbPri.name, dbPri1.name
    FROM [DbName].sys.database_principals dbPri 
    JOIN [DbName].sys.database_role_members dbRoleMem ON dbRoleMem.member_principal_id = 
    dbPri.principal_id
    JOIN [DbName].sys.database_principals dbPri1  ON dbPri1.principal_id = 
    dbRoleMem.role_principal_id
    WHERE dbPri.name != 'dbo'