At issue is whether the defence counsel can cross examine Joshua Boyle’s estranged wife with respect to the couple’s sexual history.
Mr Boyle, 35, has pleaded not guilty to all 19 charges against him.
A publication ban was lifted early in the trial to reveal one of the alleged victims is his wife, Caitlan Coleman.
The trial is suspended as Ms Coleman’s counsel seeks have a ruling by the presiding judge, which would allow the defence to introduce evidence and to cross-examine Ms Coleman on the couple’s prior sexual activity, set aside.
“We are taking the unusual and rare step of appealing this ruling during the middle of the trial because if we wait until the conclusion of the case the damage will have been done,” Ms Coleman’s lawyer, Ian Carter, told the BBC in an email.
Canada’s criminal code limits the ability to introduce a complainant’s past sexual activity as evidence in sexual offence proceedings.
But the court can make exception under certain circumstances, including whether it is relevant to an issue at trial.
The charges Mr Boyle faces include assault, sexual assault, unlawful confinement, uttering death threats and criminal harassment.
Police say all the alleged offences occurred after Mr Boyle and his family returned to Canada in 2017.
The identity of the second alleged victim remains subject to a publication ban.
In her testimony at trial, Ms Coleman painted a picture of a frequently volatile relationship with Mr Boyle and accused him of sexual assault.
Pakistani soldiers rescued Mr Boyle, Ms Coleman, and their three children from captivity in October 2017.
Mr Boyle and Ms Coleman, who is American, were kidnapped while backpacking in Afghanistan in 2012 by the Taliban-aligned Haqqani network.
She gave birth to their children while in captivity. Their rescue made headlines around the world and on their return to Canada the family was invited to meet Prime Minister Justin Trudeau.
But less than three months later Mr Boyle was arrested and charged.