First be sure you know what you actually have. People often mistake a virus for a fungus, insect for virus, bacteria for either, etc. I had a client once in a panic over this "bug" on her plant (she brought in a sample) and wanted the best pesticide. It was not an insect, but a blight and all the pesticide in the world would not have helped - and probably would have killed her plant. Biocides are a lot more harmful in the hands of the average consumer than those licensed and/or knowledgeable.
These are likely not harmful to your cham and treating them, but I'd be more concerned about a fungus than mites b/c the spores can become airborne and irritate the nasal and respiratory system, just like in humans, but less likely. They can also reproduce quickly.
IF you have spider mites you can simply take the plant outside (or into shower) and give it a good forceful; spray under the leaves and in the stem/leaf crotches.
IF you have a fungus... ANY fungus will get WORSE by adding moisture. Every droplet of water that hits the fruiting bodies will shoot the spores everywhere.
Can you say why you think they are mites and fungus? Mites thrive in a dry arid environment (therefore rarely a problem in cham setups) and fungus in a wet and overly moist. You can use a baking soda and water solution to treat the fungus, but first let's see what, in fact, you have.
Can you post decent pics of plant, setup, damage from mites/fungus?
lele
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Chameleon Help & Resource Info
1.0 Nosy Be Panther Chameleon - Cyrus
0.1 Veiled Chameleon - Luna. She's now hanging from her big jungle gym in the sky
1.0 Beardie - Darwin
1.1.1 Side-blotched lizards - Ana and Stan
0.2 felines - Kyndra and Lita
0.1 African Clawed Frog - Skippy
0.1 Chilean Rose Hair Tarantula - Rosa Leigh, Died 4/21/06 
0.1 Goliath Bird-Eater Tarantula - Natasha, donated to science 4/4/06
?.? Pinktoe Tarantula - no name yet