Dominik, there are two kinds of relative paths. A file-relative path starts with .../ and as you said, this works fine in Blue Griffon. A site-relative or root-relative path starts with / and this is apparently not supported.
I use this second kind of path in all my website links, because the link can be the same no matter where it appears in the site structure and I don't have to update links if I rearrange the site structure. In other words, the links still work if I change a page URL from /contact/email.html to /support/contact/email.html.
In order to resolve a root-relative path, the application needs to know where the root directory of the site is. The web browser assumes it's the root of the domain name, but an HTML editor needs to know what directory on the local file system is the root of the site ... something like /users/arlo/projects/mywebsite. I think the simplest way to implement this in the app would be to let users add the root directories of all their sites to a list, and then whenever they open a file, the app would look for a matching parent directory and resolve links to that.
Let me know if you think you could add this. Otherwise I'm going to upgrade my copy of Dreamweaver and continue using that.