Hey metal; Thats a classic mistake that folks make sometimes. A DPDT can definitely have a middle position. Most Ibby's use that style of switch. So do older Peaveys like my Patriot and Predator.
"Poles" refer to the number of individual circuits, or "commons" that the switch has.
"Throws" refers to the number of lands, or contacts, that that common can connect to.
Then you have handle positions which is independent of either of those.
For example, I could have a DPDT switch thats, on-on, on-off-on, or on-on-on. (Ibby/Peavey style.)
A Fender 3-way or 5-way would be an example of a DP3T switch. Two common terminals, three mating contacts. One has 3 positions, one has 5, but they're both DP3T.
Fritz; I'm just heading out the door to go to work, but I'll post a diagram when I get home tonight. In the mean time, if you feel like it, study some of the Ibanez diagrams that use a toggle-style 3-way. Thats what you need . Its a fairly expensive
switch.