The pilot and her passenger died when their Cessna hit the rear of a two-storey house in Sydney, the Daily Telegraph reported.
Assistant Police Commissioner Frank Menilli said the rear of the house was a mess, and the back patio had been destroyed.
But the mother who lived at the home with her newborn baby escaped the tragedy, because she was taking the tot to visit Santa.
Menilli said the bodies of the two women had not yet been recovered. "The bodies are in situ and it is extremely difficult to actually see their age but I expect they are in their late 20s."
A witness has told Fairfax Radio Network the plane that crashed had its tail hanging off before it came down.
The owner of the house, Stephen Cordina, told local news site the Liverpool Leader no one was at home when the plane hit.
"I haven't been allowed in (to my house) yet to see the damage, but I think (the plane) landed half in the house and half in the backyard," Cordina said.
The plane crashed on Flame Tree Street in Casula about 11.30am (AEDT). The mid-air collision happened as one of the two planes involved tried to land at Bankstown Airport.
The other plane sent a mayday call to the airport before it made an emergency landing. Its 25-year-old student pilot and 89-year-old instructor suffered only minor injuries, the ambulance service said.
The moment when two planes collided in mid-air, sending was captured in astonishing detail on a government website intended to help monitor aircraft noise.