Unable to configure Jira swimlanes

I'm currently trying to create a Scrum-ban board within Jira, but I got some difficulties. Below is what I am trying to achieve.

1. I have an expedites lane; expedites are the tasks we have to handle asap (Most of the time, they are not stories)
2. The stories are on the first column and sorted by priority
3. Each story has a set of tasks

To build this board, I currently try to configure the board to have a swimlane per story. The problem is that some stories are swimlanes, some not! I do not understand why?

Here is what I got:

In JIRA, when you select 'Stories' for swimlanes then any story that has sub-tasks will get it's own swimlane. However, stories that do not have sub-tasks or any other issue type will be shown at the bottom of the board without swimlanes.

Unfortunately it is going to be difficult to achieve what you want. Sadly JIRA only allows one type of swimlane at a time. You can use the 'Stories' swimlane approach or you can have your expedited swimlane, but you can't have both.

The best that you can achieve would be to use 'Stories' for the swimlane and manually make sure that the expedited stories are moved to the top of the board.