My family is the same way and we are Italian also. I have always kissed my cousins on the lips also. I don't anymore for some reason. I guess it's an Italian thing, LOL.

I did that with my mom and dad, and so did my siblings.
It was never a weird thing for us. It was a little peck on the lips, that's all. It signifies the deepest level of intimacy.
Intimacy and sex are not the same thing. Kiss on the lips is just the next step after hugging. I do this with my friends all the time. Guess it got passed over.
I'm Italian btw.

I kind of thought the same thing. My Dad and I were close, but we never kissed on the lips. You can tell however there is a genuine love between Tony and his daughter. That was good to see.