We have limited experience touring, but we did slog through some mud on our last trip.
For rough paved roads, dirt, and light gravel, the Schwalbe Marathons were fine for us. We used 700x35 size. We did slip and slide in the mud however.
If you really do plan to ride on large diameter gravel and significant mud, then I would suggest a tire with more tread. But probably more importantly, get as large of size tire as your frame can handle. Perhaps the Schwalbe Marathon Extreme or XR in 700x40 or larger.
Our tandem (co-motion speedster) wouldn't take larger tires and still have room fenders. Our only real complaint with the bike. If you are purchasing a tandem with plans to do a lot of rough routes, then I'd consider one with 26" wheels that will give you lots of clearance for mud and fenders.
Our dirt, gravel & mud experience:
http://www.crazyguyonabike.com/doc/CGtour2009