You can rip a full disc as an ISO file or a folder structure. That will give you the exact contents of the disc that you can store on a hard drive (local or networked), but iTunes can't play those types of files. Other programs, such as VLC can play it back, with menus and all. You can rip to this format with RipIt, but there are others out there too.
Extras in downloaded iTunes movies (and the similar feature for music, iTunes LP) are built with a framework called TuneKit, for which Apple has posted some developer information. From what I can tell, it's basically all the media (videos, pictures, music) in iTunes-compatible format (i.e. H.264 m4v for video), tied together with some HTML and CSS for the "menus".
So if you're comfortable with web development, it looks like it's possible to create your own iTunes Extras to package the content from a DVD, but you'll need to recreate the menus on your own, they can't be ripped directly to this sort of format. Extra audio tracks, commentary, and subtitles can all be ripped by standard tools like Handbrake, and deleted scenes or other video features can be ripped as separate video files, then linked in via the menus you create. There are some tutorials from Gigaom and iTunesLP.net that apply to iTunes LP, but the format seems to be pretty similar, so they may help.
So all in all, it's possible to create a similar experience to a full DVD in iTunes, but it will take a lot of work on your part. Alternatively, if you use another application, you can get the full, bit-for-bit copy by ripping to ISO files.