Runner on third with 2 out. Pass ball, batter interferes
with the play at the plate. Who is out and who leads off the next inning?

The batter is out in this situation with 2 outs.The next batter in the batting order leads off the next inning.

Jeff

Yep, and with less than 2 outs, the runner is out.

Speaking ASA

The batter will always be the player ruled out regardless of the number of outs. No runs may score after an act of interference, and if not the last out of the inning, all runners must return to the last base touched at the time of the interference.

Obviously, the next batter would lead off the following inning.