Your unlimited texting plan only covers the US. You will be charged for texting out of the country.
Here is a link to how much you will be charged.
you can get around the txt messaging charges by using your mobile IM if you have it, and then you wouldnt have to worry about it. I have my mobile app set up to where it sends me a txt message every time I get an offline message when I'm logged off of messenger.
I hope that helps!
If you are currently in the United States and he has a cell phone number from the United States then you wont see any additional charges (for instance, all Verizon will see on your end is that you sent a text msg to regular cell phone number. Verizon can't tell if your AT&T friend is in Europe or not.). If you are in the United States and he has a European number that you are texting then yes you will see extra charges on your bill. If you are outside of the United States then you will see extra charges whether he has an American number or a European number.