DO NOT mix battery types! You are asking for an explosion. The weaker battery will drain first, forcing the higher battery to drain more than it should. Overdischarge in lithium-ion batteries is very, very bad. Personally, I would throw away any batteries you've done this with already. With that emergency warning out, keep in mind that I'm not an expert personally, and I'm basing this on what others have said to me.
EDIT: Well, if you're using a li-ion and an alkaline battery, the most likely scenario is that the alkaline battery will overdischarge and leak caustic juice.