There was a similar thread on this topic.
From page 2 of "Balk with catcher's interference" topic in Rules:
Posted by umpschool:
"If I could chime in:
We teach that you enforce penalties as the provisions provide for. For instance, in order for a balk to be nullified, all runners including the batter must advance one base safely. However, if it is followed by a catcher's interference, you must first enforce the catcher's interference (if necessary) to see if all runners, including the BR advance. And that requires that you let the entire play end. Take the following play:
Bases loaded, no one out. Pitcher balks, followed by catcher's interference. The batter hits a ground ball to the shortstop in the hole, who throws to first to retire the BR. However, on the play, R2 rounds third and heads for home. He is called safe on a close play at the plate. At the end of the play, R3 and R2 have scored. R1 advanced to second base, and the BR was thrown out at first.
It seems that out of all the answers on here, none (that I have quickly glanced over) would have been correct. I've seen two camps of explanation in this thread. Let me show you how each is in error.
The first camp says that you should enforce the balk as soon as the BR was put out because they all didn't advance one base safely. This is not appropriate because the catcher's interference (listed as "or otherwise" in the balk penalty) has not been enforced. Enforcing only the balk would create this situation -- R3 scores, R2 is awarded third base, R1 is awarded second base, and the BR is returned to bat with the previous count.
The second camp insists that you enforce the catcher's interference (they're right, BTW), but that you should also kill the play right away (they're wrong, BTW). Enforcing it this way would create this situation -- The BR is awarded first base, R1 is awarded second base, R2 is awarded third base, and R3 is awarded to score. Now that all runners, including the BR, have advanced one base safely, the balk is nullified. If the offensive manager wanted to elect to take the results of the play (because he's greedy), he has the right to do so. Problem is, there are no results under this interpretation because you killed it right away.
Now let's say you leave it in play and R2 is called safe. Since they did not all advance a base safely, you enforce the catcher's interference. But now the manager comes out and says, "I want R2 to score. I elect to take the results of the play."
You would then rule on that election. R3 would score, R2 would score, R1 would be awarded second base, and the BR would be called out.
After all the runners then reach their awarded bases, all runners, including the BR, have now NOT advanced a base safely. You would then enforce the balk penalty after all. Enforcing the balk would create this situation -- R3 scores, R2 is awarded third base, R1 is awarded second base, and the BR is returned to bat with the previous count.
Once they ask for it, they can't go back. Yes, they still only have one run score, but the BR isn't standing on first base. Instead, he'll be batting again, and first base is empty. They're required to know the rules too."