It is really hard to tell from pictures. Basil is susceptible to downy mildew – especially in Florida which is caused by Peronospora belbahrii or Pseudoperonospora cubensis and can spread easily via wind-dispersed spores that it produces abundantly – confirm this by looking for  these spores which look like dark purplish grey fuzz on underside of leaf when high humidity. (For basil specific mildew see http://extension.udel.edu/blog/tag/basil-downy-mildew/)  You could also have black rot Didymella bryoniae in which case you'd have Leaf symptoms varying from browning at leaf edges and between veins which is what your picture looked like to circular tan to brown spots.  This is often accompanied by "rot" on the stem which appear as tan lesions, often with black spots and may have a dark gummy exudate (see http://www.extension.umn.edu/garden/diagnose/plant/vegetable/cucumber/leavesspots.html).  But my best guess at this point is Bacterial Leaf Spot (Pseudomonas cichorii)  (see https://growingsmallfarms.ces.ncsu.edu/growingsmallfarms-basilproblem/).  In any case, remove all of the affected leaves and take them far from your plants.  Do not overwater – all of the plants you specified are mint family and do not like to be overly wet.