As already mentioned, if bat hits ball its interference, if ball hits bat it's "nothing".
(That's a bit of an oversimplification, as there are rare exceptions to the rule. But for the purposes of this play this should be a good enough rule of thumb.)
Now, the fair or foul part...
In "non-interference" cases of bat and ball contact (ie: ball hits bat) if the contact is over foul ground then the ball is immediately foul. But when the contact is over fair territory the ball isn't immediately fair! It's "live and in play" with the fair/foul status not yet determined. That is determined the same as on any other batted ball (where ball first is touched by a player or settles, etc).
On the play in question...where did the ball go and what happened AFTER the ball hit the bat?