I guess you could technically share a mug, but I would suggest bringing or buying some kind of mug to transfer the drink into for the other person. The mugs themselves are on the small-ish side IMO, and if you put ice in it, you don't actually get that much drink in it. We filled ours frequently.
I'll also add that we never purchase the mugs at WDW, but did purchase them and found them useful at Aulani. The refill stations were conveniently located no matter where you were, and it was easier to run down and fill them up at Aulani than it is at many WDW resorts. There were a variety of options at the different stations as well.