Apple - iPhone 5 does not work while charging

The problem is the electrostatic current/charge/grounding while using Charger.

First make sure you do use the original Charger.

If your iPhone is in a leather case, remove it.

If you have a protective case, or if you are using a plastic sheet or film on the display, try removing them and testing the device without it.

Update:

I missed the point of you having 2 other devices doing the same.

In that case it could be the electric wiring in your place. Try plugging in in a another place (coffee shop). You might have what it is called High Frequency Harmonics (dirty electricity) in you home caused by number of different sources.

It sounds as if it could be a problem with the charger; I've seen a phone automatically pressing buttons etc on a touch screen device! Try using a different charger (both wall plug and cable) to see if that helps.

The fact you're having the issue on two devices suggests that it's not a device or iOS related issue.

From http://www.righto.com/2014/05/a-look-inside-ipad-chargers-pricey.html?m=1 You might wonder if the power quality actually matters. The biggest impact it has is on touchscreen performance. The interference from bad power supplies is known to cause the touchscreen to behave erratically.[16] If your screen malfunctions when plugged into a charger, this is probably the cause.

Note sixteen on that page links to a further technical explanation.

You probably have a faulty charger or perhaps even a counterfeit one. If it's not the charger, I suppose it could be an issue with the wiring you've connected to.