New cave form

Caves for the most part appear to be vertical constructs. In the real world, many, if not all, caves are more horizontal. Picture Mammoth cave. If no human hand has been involved, they seem to be between rock layers and are more side to side than up and down. Is it possible to make some of the MC cave structures more in this horizontal design? Also the 'tites and 'mites sound like an interesting idea for these caves. Perhaps limestone and slate blocks might need to be added for world generation of these caves.