If I'm on Wi-Fi, does it still charge for international messaging?

So I recently(July 24) just got the iPhone 5 (Verizon) and last night I got a text saying I already used 78% of my data allowance of my bill! Anyways, I honestly don't think that's possible because I most of the time I use my phone I'm on my Wi-Fi and supposedly it doesn't use up that much data on Wi-Fi? But also, if I text somebody that's located in the Uk (iPhone to iPhone, iMessaging only) will it still charge if I'm on Wi-Fi? Thanks! Verizon is getting me really mad with the data usage!

It's safer you turn off your data completely and just be on Wi-Fi until the month is over and your data allowance is reset again. You have to go into "Settings" then "General" then "Cellular" and turn off your "Cellular Data"

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