From building a mostly mud building in a hot humid climate, it seems that the best you can usually do is "not less comfortable than outside". Basically a large reflective (say straw) roof/shade without walls is the ideal dwelling type, open to prevailing south breezes. Humidity can be regulated a bit using appropriate partitions, but nothing too much as far as I have found.
In the end as long as there is enough of a breeze conditions can be kept "moderately comfortable" without AC for most of the year in our location. Though, it does really ask for there to be a nap in the middle of the day.
I feel great jealousy for all the creative solutions that can be used in dry climates, including convective and evaporative!