Constance is definitely "spot on" - especially re: the leaf issue. If you examine your herbs, you'll find that the ones that developed in a relatively harsh hot dry Mediterranean-type - oregano, thyme, rosemary, sage, etc. - will want/need far less water than succulent fleshy-leaved herbs like basil, chervil, parsley, etc. In fact, overwatering the Mediterranean types will quickly kill them via root-rot &/or fungal problems.
I always keep my basil, parsley, etc., soil moist. Not soggy - but moist.