Police have said a 30-year-old Australian man who died trying to save his girlfriend committed an "act of supreme courage" by leaping off a cruise liner after she fell.

Paramedic Paul Rossington fell 65 feet into the water from the balcony of a cabin he shared with Kristen Schroder during a 10-day South Pacific Carnival Cruise in 2013.

An inquest into their deaths heard that Schroder, 26, climbed over the balcony shortly before 9pm and lost her footing on a rail before falling to her death.

Infra-red CCTV footage shows that she clung on for four seconds before falling.

Video footage showed that Rossington immediately jumped in after her. Their bodies were never recovered.

"He must have known that jumping out would most likely end with him losing his life," detective sergeant Michael O'Keefe told the inquest, calling for Rossington to be awarded the Cross of Valour.

"When [he] has seen her slip, he's jumped out of bed and when she's fallen, he's gone straight over after her. That act of conspicuous courage should not go unnoticed."

An advocate assisting the coroner said the deaths of the couple appeared to be a "tragic accident".

"He has not thought about his safety at all – that is certainly an act of bravery," Erika Mulligan said.

The inquest heard the couple had a "turbulent relationship" and had regarded the 11-day cruise as a "make or break" trip.

The couple, from Barraba in New South Wales, had been on the 10-day South Pacific Carnival Cruise with friends and family.

Their disappearance was not noticed until the ship arrived in Sydney the following morning and they failed to disembark.

Search and rescue teams covered 1,360 square nautical miles before calling off the search, police said in a statement.