GH2 HDMI out on MX02 & Black Magic (Need for studio recording)
It isn't really clear what you are asking here.  The 23.9 frame rate is most likely 23.976 which is the more accurate standard frame rate for 24fps.  This shouldn't result in a stutter.  It is possible that your computer is simply not powerful enough to play the video smoothly.  

Are you trying to capture from both the Intensity and the MX02 at the same time from different cameras?  This is going to put a pretty extreme load on your system's ability to store the file and will almost certainly not work without an SSD and even that might be pushing it.

Is there a particular reason you need to be capturing the input live?  If you simply want to do uncompressed capture, I would recommend recording to Black Magic HyperDecks and then syncing in post.  Alternately, if you need to be doing live editing, you could get the Black Magic Studio ATEM Production Switcher which would handle what you need.