I assume the subway system is the same thing as the "underground railway" or the U-Bahn, so I wouldn't worry about that.
Yeah, the thing is I don't know if U-Bahn tickets can also be used on normal, above ground tickets. Or if you can buy certain tickets that will let you do that. Your best bet is probably to just call the fine folks at
Die Bahn [DB] - Startseite Reiseportal: Auskunft, Fahrkarten, OnlineTicket, Urlaubsideen. I'm sure they have english-speaking representatives.
Sorry I can't be more help but this isn't really one of my better subjects.