This can technically sort of be done with a bunch of setup, but it involves a static IP address and/or a dynamic DNS provider.  If I really needed this, I'd forward the appropriate ports and set up Apache.  Other options can become more involved, but they're not common-you'd possibly have to do some hacking and write a couple programs.
The issue is that, without btsync, you can't reliably get an external connection.  Btsync is doing magic that's beyond the scope of this thread to let you not have to port forward.  I doubt you'll find exactly this-if the files aren't on an external server and if you aren't using custom software on both ends, it's possible, if you know what you're doing and don't mind getting your hands dirty, but far from simple.