Honestly, I stopped planting anything that needs frequent water or consistent moisture in terra cotta. I use them outside quite successfully, but even with my air circulators going inside, my humidity can get so high the pots get a (harmless?) mold on the outside.

I haven't gotten it on my soil surface, though, which makes me think you might be overwatering or lack airflow. Keep in mind some mold will attract fungus gnats, which can carry damping-off disease, though that's usually a problem with seeds/seedlings. Depending on your herbs, they'll be fine with low humidity and don't need a greenhouse.

I do have spider plants, an aloe, snake plants, a gloriosum, and Vick's plants in some indoors without issues, because I water those every other week at the moment. I will say that most of my plants indoors grow better in plastic, sadly, or glazed pots, which is probably a me issue. Including the spider plants and snake plants! But I do not have mold issues with plastic/glazed, which seems counterintuitive.

Also, I suspect the higher-fired/frostproof terracotta is less susceptible to mold, but I have no evidence/proof of that. Check to make sure the mold spores aren't coming from elsewhere in your house (shower room, etc.). I also recommend baking or using a bleach solution on any new pots you get from the store, if you aren't already. Though I will confess I didn't bother on my 70cm behemoths outside ;)

I know a lot of people grow successfully in them, though, and hope they have some advice for you!