I think you're just missing the SET FMTONLY OFF setting

SELECT a.* INTO #hdr FROM OPENROWSET('SQLNCLI','Server=(local)\SQLEXPRESS;Trusted_Connection=yes',

'EXEC(''SET FMTONLY OFF RESTORE HEADERONLY FROM DISK =''''c:\code3Billing\ClientSQLData\Master\code3billing.bak '''''')') AS a