As above. If you are talking about Blu-Ray disks, then all MKV does is transode them in order that they can be recognised and run through Handbrake...so the workflow for BRD's is thus:
BRD to MKV making sure you choose the right title, they've improved things by pointing you at the right file..usually, but not always the largest. Untick all except the title that is designated primary ( you may find you have to do this over until you get the idea of which title is which, bit the small ones are obvious)
The output can then be run through Handbrake using the preset of your choosing.
Handbrake is free....MKV is around $20.00 but well worth it.
After that I copy the checked output file ( I use VLC to ensure I have the correct audio and file size) to my R4 and my 4TB Seagate USB3 drive.
Using Air Video Server, I can then stream to both my ATV units at will.