IPhone getting charged for 3G use?

I just recently got an iPhone 4. I have a 2gig data plan. I use Wi-Fi whenever I can but if I don't have Wi-Fi and am therefore connected to 3G, I don't go on the Internet. However, Verizon has notified me that I have used 50% of my data package for this month. I thought using Wi-Fi made it so it DOESN'T go against my plan? Even though I don't use the Internet with the 3G, am I still getting charged for being connected to it?

Added (1). (With verizon)

Go into your settings, and into general. Tap the "cellular" tab and make sure that at the top "cellular data" is turned off. When it isn't turned off, and you're connected to wi-fi, there are still things that the cellular data does. Also, go into the "safari" settings and turn off the option to use cellular data to save reading list items.

If these are already turned off, maybe Verizon is making a mistake. Wi-fi doesn't use your cellular data, and shouldn't count towards your cap.

Do you have facebook/twitter? Email? Apps from the app store?

These will access data without your permission whenever there's a connection, regardless of Wi-Fi or not. A lot of people forget that apps have agreement you click yes to when downloading, they typically say something along the lines of data use in the background.

You can go into settings, mobile network and switch off the mobile data until you locate what is running without your knowledge. Grab a data counter from the app store next time your on Wi-Fi to monitor your data and see where it is coming from.

Wi-Fi isn't part of your bill. Verizon has been having data problems. Either go to a store or go to settings, click general, and then click about. A screen should pop up and you can follow those instructions