As you have discovered, HandBrake does not deal with the menu ( intro) that is created within iDVD.
Rich is correct when he says that there is a VOB file that includes the menu.
However, if this is converted in HandBrake then it will not be interactive like the menu in iDVD is.
If you bring back your Mp4 files from HandBrake with chapter markers into iMovie then I do not believe that iMovie will see these chapter markers. So trying to merge a Handbrake converted intro VOB with these files in iMovie would mean you would have to re-insert all the chapter markers again before export. Could be a big job.
Obviously having the Mp4 files from HandBrake enables you to play back your movies on your Mac and other devices.
If you were only wanting to play back the DVDs from your Mac without having to insert the DVD into an optical drive, then you could create a disc image of that DVD by using Disk Utility which is on your Mac.
The disc image is a copy of the DVD on your hard drive ,complete with menu,and is played back just like a DVD in DVD Player.
To make a disc image of a DVD put DVD in optical drive and close DVD Player if it opens.
Open Disk Utility and point to your inserted DVD.Then File>New Image> Image From DVD.
Set Format to DVD/CD Master and Encryption to None.
When you have created the image double click on it to mount it and then open DVD Player to test.
If you want to preserve your home DVDs then it is a good idea to create an image in any case.You can burn a copy onto a DVD from the disc image using Disk Utility at a later date if required.
