A previously unknown group - the Green Brigade, member of the 1920 Revolution Brigades - claimed responsibility for downing one of the helicopters.
US officials said on Thursday that 18 soldiers had been killed since US-led troops launched their latest attack on Falluja on Monday.
Aljazeera also reported that five Iraqi national guardsmen were killed while another 34 were wounded since 9 November.
In a sign of mounting US casualties, 102 American soldiers seriously wounded during the Falluja offensive arrived in two planeloads at the US' main European military hospital in Germany, a hospital spokeswoman said.
The hospital has expanded its intensive care unit and medical surgical wards to cope with the stream of patients.
Two more planes of wounded are due on Friday, spokeswoman Marie Shaw said.
The US military said the total number of wounded as of Thursday morning stood at 178. It also said several hundred anti-US forces were killed in Falluja.
"This is one of our peak periods. We are very busy. It is more than we have seen in the last couple of months because we used to admit about 30 patients a day," Shaw said.
Increasing numbers of wounded
US troops are being evacuated
Thursday's arrivals joined 125 wounded who arrived from Monday to Wednesday, including 70 on Wednesday.
Landstuhl is the usual destination for seriously injured US troops stationed in Iraq or Afghanistan.
"They have all kinds of injuries - explosion, blast injuries, gun shot wounds," she said. It was possible that some intensive care patients had also suffered amputated limbs, she added.
Upsurge in violence
In other developments, Aljazeera has learned that four Iraqi policemen were injured as a result of an explosion of a booby-trapped car driven by a bomber in central Hilla city.
Another car also exploded inside a petrol station along the highway between Hilla and Musiab.
Also on Thursday, the police chief of Babel province escaped an assassination attempt carried out by a group of armed men.
The attack on police stations in
Mosul seemed well coordinated
And in one of their most daring attacks to date, masked fighters stormed six Iraqi police stations in Mosul, 370km north of Baghdad, seizing weapons and torching buildings.
Groups of men pulled up in front of police stations in various parts of the city on Thursday, forcing policemen out in what appeared to be a coordinated attack.
Dozens of people were seen fanning out on the city streets and some took cover behind sandbags and were seen firing mortar rounds on US and Iraqi forces stationed on four of Mosul's five main bridges.
Speaking on Monday, the same day that the massive attack was launched on Falluja, Iraq's Defence Minister Hazim Shaalan vowed a campaign would be launched in Mosul.
"We will launch operations in Mosul, because some groupings that came from neighbouring western countries are trying to step up terror operations there," he said, referring apparently to Syria.
A US general also hinted at further offensives after the battle for Falluja - the largest military operation since last year's US-led invasion.
Mosul has seen a rash of car bombings against Iraqi and US forces in recent weeks.