There is no problem in calling a non-Muslim by my brother's word.

exactly the contrary,

it's respectful and appreciated to calling a non-muslim by my brother's word or sir, etc..

and be friendly with him to give him a good picture of the Muslims.

that is what Allah Almighty ordered us to do.

Evidence of this in Surat ([(17) **Al-'Isra'**][1]) Chapter number [**17.53**].

**" Tell My worshipers, that they should say words that are the finest ".**

**In Arabic:** (**سورة الإسراء** الآية رقم **53**)

**"وَقُلْ لِعِبَادِي يَقُولُوا الَّتِي هِيَ أَحْسَنُ"** 


But on the condition, that doesn't exceed the limits stipulated in Islam, between the girl and the non-mahram whether he is a Muslim or not.

**summary** 

call non-muslim or Muslim by my brother's word
it's just word to express the respect and appreciation.
and don't cancel the sanctity(Hourma) between of the girl and non-mahram from men.


I hope my answer is clear. 

  [1]: http://www.e-quran.com/language/english/english4/r-sura17.html