Add-ons using the techniques described in this document are considered a legacy technology in Firefox. Don't use these techniques to develop new add-ons. Use WebExtensions instead. If you maintain an add-on which uses the techniques described here, consider migrating it to use WebExtensions.
From Firefox 53 onwards, no new legacy add-ons will be accepted on addons.mozilla.org (AMO).
From Firefox 57 onwards, WebExtensions will be the only supported extension type, and Firefox will not load other types.
Even before Firefox 57, changes coming up in the Firefox platform will break many legacy extensions. These changes include multiprocess Firefox (e10s), sandboxing, and multiple content processes. Legacy extensions that are affected by these changes should migrate to WebExtensions if they can. See the "Compatibility Milestones" document for more.
A wiki page containing resources, migration paths, office hours, and more, is available to help developers transition to the new technologies.
When dealing with the facilities of nsIURI, the task of parsing a URI can still require additional work.
It's advised that you use the nsIEffectiveTLDService.
Grabbing the main domain using the EffectiveTLDService
Even using the ETLDService, you're unable to get just the base domain sans TLD. So, here's some sample code to determine the base domain without any suffixes:
var eTLDService = Components.classes["@mozilla.org/network/effective-tld-service;1"].
getService(Components.interfaces.nsIEffectiveTLDService);
var suffix = eTLDService.getPublicSuffix(aURI);
var basedomain = eTLDService.getBaseDomain(aURI); // this includes the TLD
basedomain = basedomain.substr(0, (basedomain.length - suffix.length - 1)); // - 1 to remove the period before the tld