I disagree with Kingledion's answer. Yes, the general atmosphere would work like he wrote, however I believe the floating islands will interfere with the development of high and low pressure systems which form the backbone of the hadley/ferrel cell circulation.
The floating islands, while not continent sized, will create shadows on the surface of the planet. This will create areas of cooling. The surface of the floating islands will warm up due to reflection of sunlight and the heat transpired by any plants and animals. This will affectively bring extra warmth to the middle - upper regions of the atmosphere (depending on how high they are floating).
On the surface this will create areas of low pressure in the island shadows, and areas of higher pressure in areas with direct sunlight warming the surface. On the floating island surface, there is also isolated areas of higher pressure and areas of cooler pressure in the open air.
So now you have three dimensions to take into account; (1) the 'horizontal' surface to surface dimension, (2) the 'vertical' atmosphere to surface dimension and (3) the 'horizontal' atmosphere to atmosphere dimension.
The surface generally warms more at the equator than at the poles. So localised shadow affects will change the way that the wind and atmosphere moves. If there are more islands concentrated in a certain latitude band at specific times (as suggested by Kingledion), this will result in more shadows on the ground, resulting in a cooler than expected ground temperature.
(1) This will result in surface low pressure systems in areas that would normally be experiencing high pressure systems. eg if a low pressure system forms around the equator because of the islands, air will end up flowing from the midlatitudes towards the equator, instead of away from the equator as it does now on Earth. So wherever you have a concentration of floating islands, the surface winds will change in accordance - wind blowing from the sunlight warm areas to the cooler shadow areas.
(2a) This will create a strong pressure differential between the cooler surface than the warmer floating island tops. Wind moves from areas of high pressure to low. So you will have stronger downward winds wherever there are large concentrations of islands. (note, even though 'heat rises', air temperature does cool with altitude. About 1 degree celsius for every 100m. I doubt you will get equator surface temperatures on your equator floating islands, but the temperature will be warmer than expected at that altitude in comparison to Earth).
(2b) Winds pulling cold mid to upper atmosphere air down to the surface is what normally happens at the poles. It is one of the reasons why it is so cold there. But if you have floating islands at the poles, they may break the airflow, as well as bring slightly warmer air (from transpiration and albedo reflection etc) to the mid to upper reaches of the polar region. This could result in slightly warmer sinking polar winds (only slightly, as the poles are still terribly cold due to lack of sunlight for 6 months of the year). This might actually result in more snow fall, as for snow to fall temperatures need to drop to below freezing and then rise again. So you can expect more winter snow storms in your polar regions. But also a slightly warmer summer, so you still have to worry about global warming as a whole.
(3a) Winds will also blow from the islands warmer center towards the outer ridges of the islands into empty space. So winds will be blowing off the islands and then be pulled down (might want to erect some fences along the edges for any toddlers).
(3b) Warm air doesn't mix well with cold air. It generally creates very big storms. Think hurricanes. A steady source of warm air in the typically cooler mid to upper atmosphere will feed upper atmosphere storm systems. Resulting in more rain falling to the surface or at least around the edges of the floating islands.
So you can see, if you have large 'concentrations' of floating islands, this can mess with the local atmospheric pressures. If this happens, I believe you will still have the Hadley/ferrel circulation cell system, but it will be weaker. Less warmth rising from the equator surface and slightly less cold sinking at the poles. This will impact the strength of the overall resultant atmospheric winds systems, the general atmospheric winds like the jet streams etc will be weaker, and prone to disruptions from the ever changing nature of the floating islands below them.
But never fear, if a large concentration of islands does develop, a once in a 100 or once in a 1000 year storm will come along and break them apart scattering them in all directions. And you can start all over again.