The families have asked the Ontario Court of Appeal to let them challenge last month's lower court ruling allowing the projects to go ahead.
They argue their case is of wider significance to the public and includes whether the turbine-permitting process is constitutional.
"The proposed appeal raises issues of first instance in Ontario and affects all Ontarians given the proliferation of wind projects in the province," their supplementary notice of motion for leave to appeal states.
According to the motion filed this week, the main problem is that the province's Environmental Protection Act allows the government to act "without regard to public health and by denying citizens a means of relief in the face of a reasonable prospect of serious harm."
In December, a three-judge Divisional Court panel in London, Ont., rejected that idea. The court refused to undo permits for the wind farms — one of which will be among the largest in the country, with 140 turbines near Goderich, Ont.
The Drennans, Dixons, Ryans and Kroeplins worry the turbines pose potential health risks that increase the closer they are to their homes.
Currently, the rules do not require wind-farm companies to provide reports on any public-health impacts, the motion states.
In addition, they say, once a permit has been issued, citizens can only have them overturned before the Environmental Review Tribunal if they can prove the turbines will cause serious harm to their health or the environment.
"This case thus represents the opportunity to rule on whether this test legislatively permits violations of Section 7 of the Charter by denying citizens relief in the face of a reasonable prospect of serious harm to health," their motion states.
The families want the Appeal court to look at recently released results from a Health Canada study which found wind farms can cause "annoyance," which in turn can pose a health risk.
Project proponents, which include multinational giant Samsung, maintain the wind farms are safe, and were properly approved according to all the rules after relevant consultations and studies.
In its ruling, the Divisional Court panel found the review tribunal had made no errors after considering evidence related to the turbines.
"That evidence was to the effect that causal conclusions based solely on self-reported health problems were scientifically speculative and likely misleading," the court said.
Separately, the Ontario Court of Appeal is still deciding on a request from a wind-power company to nix an earlier ruling banning turbines from an area of the Lake Ontario shore because they pose a hazard to at-risk Blanding's turtles.