It varies with the classification.

For example, the Free Wind and the mentioned battleships are large, open-deck vessels with the majority of the space being below deck but a large cabin above deck (think like a futuristic galleon). Whereas an Interceptor-class ship is not open-deck and resembles something more like the Great Fox from Star Fox. But really, it varies greatly. Particularly outside Crucible territory where people can just build their own makeshift airship (though those are often hunks of junk).

Typically, the most common shared feature is that airships will have two to six "solar rails" which are like thin wings that protrude from the ship. These not only collect solar energy but expel it backwards, giving the ship it's propulsion. They also have aura generators somewhere inside, which collects aura from panels along the bottom of the ships. The generators then run into a separate kind of mechanism along the bottom of the ship to give it lift.

Even though those are the typical features of a ship, they aren't a guarantee. Older ships go without the aura generators and short-distance vessels like skiffs don't have solar rails. And some ship designs are wacky enough to not have either yet somehow function (we'll see a few of those in the future).

In short: airships have a lot of variety.