In JIRA 6.1.x, it appears no longer possible to configure an application link whose public 'display' URL (eg. "https://jira.company.com") is different from its internal 'application' URL (eg. "http://jira.localhost"). The base URL is used for both. This is a regression from 6.0.x, where it was possible.

Workaround

The current workaround is to set the BaseURL of the applications to the URL you want to create the link with, then create the link. The Application URL for both applications will be their BaseURL. You can then set the BaseURL back to the correct user-facing URL, and edit the Display URL of the application link.
This behaviour is present in Applinks 4.0. You can see the versions of our software that contain Applinks 4.0 here.

JIRA 6.0.x applink workflow

Here's how it used to work in 6.0 and earlier (screenshots from the Adding an Application Link docs, which haven't been updated).

First specify the application URL - ie. the internal URL (notice the non-standard port):

In the next step, one could set the reciprocal application URL (as the docs say, "override the base URL specified in your remote application"):

Finally, if the application URL != display URL, one could edit the applink, and set its Display URL explicitly:

JIRA 6.1.x applink workflow

Say we're in https://jira.mycompany.com, wishing to create an applink to http://confluence.localhost, with display URL https://confluence.mycompany.com. We fill in the URL:

and..

JIRA has ignored the URL you entered (http://confluence.localhost ) and instead used the base URL. There is no opportunity to override this. Nor can this be first by editing the applink afterwards, as the application URL is unchangeable: