Strictly speaking, a sister-in-law's husband is simply referred to as the spouse's brother-in-law, presuming that the sister-in-law in question is the spouse's sibling. There is no direct relationship with the proband, a term used to describe the person or point of view when comparing familial relationships.
An in-law relationship can only occur within one degree of the proband. A brother-in-law can only be the spouse of the proband's sibling or the sibling of the proband's spouse. This is why the relationship is defined in terms of the spouse. If, however, the sister-in-law is the sibling's spouse, then her husband is the brother from the proband's point of view.
This rule is generally considered true in most English-speaking societies. However, in some regions of India and in some Indian languages, including the English-speaking Indian societies, family relationships are defined in a more detailed fashion. There is a specific word that has been coined for the relationship of the man married to a spouse's sister: a co-brother or co-brother-in-law. In many Indian languages, the word is either shaddaka or sadoo and is used for either the spouse's elder or younger sister's husband. There is no equivalent term for the wife of a sibling's brother, or in other words, no co-sister or co-sister-in-law.