Expression-Link two check-box controls but inverted, so on/off off/on...

I would only use one checkbox to control two layers. If one of the layers is named Master then the expressions would look like this:

// Layer with Checkbox
if (effect("Checkbox Control")("Checkbox")== 0)
	0
else
	100

// layer below the layer with checkbox;
ref = thisComp.layer(index-1);
if (ref.opacity == 0)
	100
else
	0

This eliminates the possibility of having to write additional code that looks for both checkboxes to fix the problem you get with both checkboxes set to on or both set to off.

If you have multiple layers, a Dropdown Menu Control would be a better option. Put it on the Master layer, then stack the other layers below and add this opacity expression to all layers you want to control. The only other editing you need to do is to add enough items to the list to count all layers.

Ctrl = thisComp.layer("Master");
sw = Ctrl.effect("Dropdown Menu Control")("Menu");
num = index - Ctrl.index;
if (sw == num + 1)
	100
else
	0