This woman is not your mahram

I would like to know what is my relationship to my brother-in-laws (wife's brother) wife. She calls me brother and I treat her like my sister. Is this allowed in Islam. Please advice.

Praise be to Allaah.  

It is not permissible for you to treat your wife’s brother’s wife as your sister, because she is not one of your mahrams. So it is not permissible for her to appear before you without proper hijab, and it is not permissible for you to be alone with her, or to shake hands with her, or to look at her, or to speak to her except from behind a screen, when there is no fear of fitnah (temptation). Allaah has forbidden the believing women to show their adornment except to specific people. Allaah says (interpretation of the meaning): 

“…and not to reveal their adornment except to their husbands, or their fathers, or their husband’s fathers, or their sons, or their husband’s sons, or their brothers or their brother’s sons, or their sister’s sons, or their (Muslim) women (i.e. their sisters in Islam), or the (female) slaves whom their right hands possess, or old male servants who lack vigour, or small children who have no sense of feminine sex. And let them not stamp their feet so as to reveal what they hide of their adornment. And all of you beg Allaah to forgive you all, O believers, that you may be successful”

[al-Noor 24:31] 

You are not one of the people mentioned in the aayah, so this ruling does not apply to you. And Allaah knows best. 

See also question no. 5538.