Was the Space Shuttle aerodynamically neutral while piggybacking, or did the combination act like a giant biplane?
This podcast with one of the pilots answers just about every question on the shuttle carrier you could have and it's worth a full listen. But to cover the flight dynamics, I would skip to 50:33 minutes, where the pilot states (please note there is no official transcript of the podcast and I typed this as I listened to it, please see the official podcast for the actual verbiage, but this is close): 


  Markus Voelter (Interviewer): Let's talk a bit about the flying characteristics, did the wings of the shuttle add some extra lift or
  was it mounted with essentially 0 angle of attack?
  
  Arthur C. “Ace” Beall (Pilot): It was mounted with some angle of attack, you can see that as it's sitting. At the speed we were flying,
  the carrier itself was about 5 degrees nose high. The shuttle was creating lift, but
  how that affected it aerodynamically is hard to say, it was always
  mounted the same way so we had no basis of comparison. It did, however,
  create a lot of drag and made the aircraft very top heavy so bank
  angles were limited.


So some lift was generated but at the speeds they were flying, other limitations came into play that were more of a concern. It's also worth noting that when in transport no one was in the space shuttle and the control surfaces were not used in any way.