I think it is appropriate to call him your brother.
Brother in law is commonly used. However, he really is no relation and should officially be introduced as your sister-in-law's husband.
There is no specific word for the husband of your wife's sister. If you need a phrase, call him your "sister-in-law's husband."
sisters in law
Husband call wife like Tarzan call Jane. :U
She is your sister-in-law.
Brother-in-law.
Your sister-in-law.
your brother-in-law :)
Unless you are in a polygamous marriage, you are your husband's wife, so you would call her your mother.
A husband's stepfather is a step-father-in-law to your wife, but, if your wife is comfortable she can still call him dad and if not, she can call him by his first name.
Phillipp uncle
There is no specific word for the husband of your wife's sister. If you need a phrase, call him your "sister-in-law's husband."
Your Brother in law's wife