(1) By mutual agreement, two or more adjacent counties may unite to create a district board of health. First- and second-class cities located in those counties may elect to be included in the district.
(2) A district board of health consists of:
(a) one person appointed by the county commissioners of each county in the district who serves at the pleasure of the appointing commissioners;
(b) one person appointed by the governing body of each city that elects to be included in the district who serves at the pleasure of the appointing governing body;
(c) additional members appointed by the county commissioners of each county that participates in the district board as mutually agreed upon who serve at the pleasure of the appointing commissioners.