To play 3D movies on an Apple TV requires you to convert the files into a SBS (Side By Side) or TTB (Top To Bottom) format which is then decoded by your TV to play. As far as I know, Handbrake does not support this functionality.
I personally do not have any experience in the field, but a google search on converting 3D blu rays to a SBS MKV should get you started. Once you have the SBS MKV made, you can then put that file into Handbrake to put it into an MP4 file.
To expand upon this, when you have a 3D blu ray, it is actually encoded into 2 separate videos, one for your left eye, and one for your right eye. The blu ray player will then decode them and play them alternately frame-by-frame (first showing right image, then left, then right, and so on). The ATV does not support this as it does not support 3D natively. Doing a SBS image has both the Right and Left image in one frame and then your 3DTV will do the work from there.
Sorry I cant be much help on this, but google SBS 3D and it will help you get started with all you need to know. Alternatively, hopefully someone here knows a lot more about the subject and can get you going. 😀