When using FaceTime on your iPhone are you charged with airtime or is it free using wifi?

There are no air time charges if you are on WiFi. If your carrier supports Facetime over cellular data, and you are not on WiFi, then you will use cellular data.

The iPhone defaults to a Wi-Fi network if one is available and you are connected to it. So if you have Wi-Fi then the FaceTime will go over Wi-Fi on your end of the conversation.

If your carrier supports FaceTime over cellular and no Wi-Fi is available then the FaceTime call will indeed eat into your usage allowance. You can turn this off in settings to prevent FaceTime over cellular.