He's clearly not Italian

What are you talking about?
A) He's an actor. And a good one. He can play any roll. Did Greeks complain when Anthony Quinn (a Mexican) played Zorba the Greek? NO. He's an actor and he acted his ass off. Did people complain when Kirk Douglas (a Russian Jew) played Spartacus (a Thracian; current day Bulgaria)? NO. He's an actor and he acted his ass off. Did people complain when Liam Neeson (an Irishman) played a German in Schindler's List? NO. He's an actor and he acted his ass off.

B) He is not regularly cast as an Italian. His major roles have been Shane Walsh (The Walking Dead; a Welsh or sometimes Irish name) and Frank Castle (not an Irish name in itself. In the comics his original family name is Castiglione, but in the TV series, it was never established that the Punisher was Italian. The Punisher was also played by a Swede (Lundgren) an American of [per Wikipedia] Irish, Scottish, and some German Jewish and Native American descent) and an Irishman (Stevenson).

C) Other characters played by Bernthal have varying, Italian, Irish, Jewish and Hispanic names.

I usually don't feed the trolls, but your comment was especially stupid.
Thank you for the comment though, because I can now add you to my ever growing IGNORE list.

That's a boxer's nose. It's obviously been broken at least once.

He looks Greek to me. I know a few Greek guys who look just like him. But not really Italian looking.