The alliance said one service member died in an insurgent attack on Saturday, while the other two were killed by bombs on Sunday. All three died in the south of the country.
NATO statements did not provide further details on the attacks or the nationalities of the killed service members.
The deaths raise the number of international troops killed in September to 24. A total of 429 members of the international military coalition have died so far this year.
The narcotics raid took place Saturday in Baghran district of Helmand province, according to NATO forces. The alliance described the laboratory as one of the biggest heroin-producing facilities to be destroyed in Afghanistan in the past five years, and said its profits were used to finance attacks on security forces.
It said the patrol of Afghan and coalition forces was fired on by snipers and returned fire before destroying the facility.