Question

The batter is out on strikes and if he interfered with the catcher, then the runner is out too.

Just because the batter was out of the box in front of the plate, it is not automatic interference, and contact is not required for interference.  The only required element is an attempted throw by the catcher - no throw attempt, no interference.  However, if the batter is out of the box in front of the plate, and the catcher attempts a throw, the benefit of the doubt is certainly going to the catcher.

In any event, if the plate umpire judges batter's interference, it should be called right away, and the play is allowed to continue.  If the catcher's initial throw retires the runner, the interference is ignored.  If not, the batter is out and the runner returns. In your example, the batter was already out on strikes, so the runner is out for the interference of the batter.

N.B.  Unlike other rules codes, under Federation rules, the second out is not automatic when the batter interferes after he strikes out.  It is umpire judgement.

Thanks, that is what I thought.

I've been taught BORR Batter out runner returns. But as Dash had batter and runner both out..Dash as usual nailed it!

That would be correct, but when the batter is already out (as in the OP,) the runner is declared out.

In OBR the runner is definitely getting banged. In HS the umpire gets to judge if the runner may have made it. If so he just goes back, if not he is called out. I was protested on this very call last year. I banged the runner, the coach brought up the option and I told him the runner is still out. The only way he isn't is if it is obvious to all he had it. I have yet to see it happen. 

Great post and discussion! Thanks for the bump in baseball IQ.