It looks like a green mold on the branches, not leaves, and going from bush to bush.
Azalea Bush Disease
Certified GKH Gardening Expert
I suspect that the "green mold" you have on your azalea branches is actually lichen. Touch it - is it relatively hard and crusty in appearance? If so, no action on your part is necessary as lichen are not harmful. If you want to remove it, it can be removed, gently, with a soapy solution.
For more information on lichen, please visit the following link: