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If you charge a parent unit, at what point do yu decide if/when
you have a multiple charge on both the parent unit and the Free Company,
and when do you decide it's a single charge and the Free Company
has the opportunity to counter charge?

The mechanics for the countercharge are deliberately simple. First you get stuck in to the parent unit. Then, if the detachment can see your flank, they can hit you in the flank. Normal rules do not apply.

The countercharge rule states: 1)After moving chargers, but before remaining moves, the detachment can declare a normal charge against the enemy. 2) If the detachment can draw a line of sight to an exposed enemy flank, and has enough movement to reach it, it can charge the flank, even if it would normally have to charge the front. (Empire book, p.39)

So I would say, you declare your charge on the parent unit. Move your models into proper base-to-base alignment with the parent unit. If you are in contact with the detachment after you align, I'd say it's become a multiple charge. Boo to the Empire player for sloppy positioning!
If you don't touch the detachment, then they counter-charge after you are all nicely stuck in to the parent regiment.

Cool. So I can tie up the Free Company all I like!

Classic anti-empire tactic: charge the detachment. Parent regiments (and other detachments) cannot counter-charge.

So I decide the lineup as well as whether or not the charge
is on 1 vs. 2 units, am I right?

Not sure what you mean by 'lineup'. You can only charge against one unit, and you must maximize models in contact with that unit.

If, for example, skirmishers charged a 5-wide formed unit, you would line up seven across, to get in two more skirmishers corner-to-corner (assuming 7 skirmishers had enough movement to do so). If one of those corner skirmishers touched a detachment, then you would have a charge against multiple units, and even more skirmishers would join the front rank, to try and get all the way across the detachment's frontage too.

You couldn't hit the parent unit in the middle, with half of your unit hanging off to the left, in order to try and hit a detachment as well.

But in general, you do not have to declare a charge against the closest unit... you just risk getting stranded in front of a closer unit if your target flees.

There's a reason why any half-competent Empire General keeps his detachments 2" back from the parent regiment.

It helps them not getting drawn into a combat.

In this case the opponent needs to have 2 units to neutralise the detachment. The original to charge the Parent unit and another one to keep the detachment busy.