I have this set up for Firefox 3.6.13 under Ubuntu 10.04.
- define an edit:// URL user protocol in Gnome
- Firefox then honours this user protocol
- the URLs point to local files that jEdit can meaningfully edit
- create a bash script to correspond to the command specified to Gnome
- the bash script then invokes jEdit in server mode to display the file at the specified offset.
I can supply more details if you have a similar configuration.
For Firefox under Windows I think you have to use the registry and I have no idea about other browser/platform combinations.

The catch with this is that if you edit the source file so the line numbers change then you have to update the line number in the URL that the browser displays. What I have done is to specify unique character strings in the URLs. The unique character strings are generally stable between edits. The bash script calculates the line number (with grep) before invoking jEdit with the +line: parameter. This solution will only position to the correct line for the last saved version of the file. To catch the absolute latest version in the jEdit buffer would require running macro at startup which was beyond my current knowledge of jEdit. A jEdit feature I would like to support this is the ability to pass a parameter to a macro on jEdit startup.