Half American?

Today we started discussing the US studies centre at lunch and got on a very interesting topic. One of my Australian classmate's told me that she's half American. Meaning her mom is American and her dad is Australian. She actually has dual citizenship and passports for both countries. This launched a big discussion about whether American is a nationality (versus an ethnicity). Now, most of the time in the US if someone asks "What are you?", obviously I am a European mutt. But hypothetically we asked what if you moved to Australia and had a kid here. Doesn't it sound weird to say that your child is half American, half Australian? Both are immigrant countries! Then this got us on the topic if a Canadian married an American, would that kid say it was half Canadian? Doesn't it just sound weird? Anyway, just some musings as I'm up in the middle of the night doing homework :) Have a great day!