Hiya!
What CooperDragon said.
To elaborate though, I do have a background in microbiology... Recently got me BS in it.
Can the two animals spread disease to each other? Absolutely.
Is it likely? No.
Make sure to clean up any poops/urine and saliva and you're probably good. Most mites/external parasites should be fairly different between mammals and reptiles, but there's no guarantee. Don't let them share food or water, and don't let them come in contact with "wet" contamination from each other. Wash your hands between handling one and the other.
Heck, really just wash your hands as often as you can, lol! DON'T use "antimicrobial" soap, it's actually causing a lot of problems... Regular soap is fine, just make sure to actually "scrub" your hands for 30 seconds - seems like forever but it's very much worth it, the scrubbing with a gentle, skin-friendly soap is what actually gets rid of the bacteria. Clean underneath your fingernails while washing your hands ever once in a while too. Hand sanitizer is a perfectly acceptable alternative every now and again, but it WILL damage your skin if over used and doesn't kill certain types of germs (spores especially).
Honestly if both your pets are healthy they're probably fine even if you don't wash, but might as well play it safe.
Hope that helps!
-Ellen