They don't fall through the decks because that would be a really lame episode.
It has not been explained, but I would speculate it has something to do with the gravity plating in the decks. That they weren't floating around the ship would suggest that artificial gravity has some effect on multiple phases of matter.
You might as well also ask how they were breathing the air on the ship.
It is shown that they can only push their extremities through solid objects by applying extra force, such as when they kicked the Romulan through the exterior bulkhead.