Daniel Duggan was arrested at the behest of the US government in 2022 at a supermarket in regional NSW, where he lived with his wife Saffrine and their six children.
He has been in custody for three and a half years - nearly half in solitary confinement - over claims he breached US arms trafficking laws by training Chinese pilots in South Africa between 2010 and 2012.
Duggan denies the allegations and has for years resisted attempts to return him to the US to face charges, most recently in the Federal Court.
But the former fighter pilot's appeal against the decision to approve his extradition was struck down in April.
Saffrine Duggan announced on Monday the family had lodged a challenge against the Federal Court decision.
"(We) will be continuing in our fight for Dan's freedom and Australia's sovereignty," she said on Instagram.
"This is about my family and all Australians."
The appeal will be heard by the Full Federal Court at a later date.
Ms Duggan argued then-attorney general Mark Dreyfus approved her husband's extradition to the US despite him being an Australian citizen who "broke no law" while working in South Africa in 2012.
Duggan had no criminal record or violent history but had been locked up for years without facing any Australian charges, she said.
The former US marine pilot has been kept in a maximum security prison in central NSW, about 100km from his family since his arrest.
Ms Duggan repeated her calls for the government to intervene in her husband's case as she prepares for the next stage in the family's fight against extradition.
"It's time for Dan to come home," she said.
In a letter from prison, Duggan previously wrote that he believed his activities were not illegal, and Australian and US intelligence services were aware of his work.
His years-long legal battle has taken a crippling financial toll on his family, who estimate their legal bills total about $500,000.
Duggan has been refused Legal Aid, while an injunction placed on his family's half-built house means they can neither sell it nor live in it.
"We have been stripped of our property and we have been financially devastated by our ongoing fight for justice," Ms Duggan said.
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