What I found is that once I installed the cable box as a device in LMCE, Myth kind of "figured out" that the box is where the channel gets changed.
You do have to have some type of controller for the cable box (UIRT, Serial, etc.) Once I got the box and UIRT setup then asked Myth to change the channel, the actual tuner card stayed on channel 3 and the cable box changed to the channel I wanted.
On a side note: There is considerable lag using the UIRT to control the cable box (1-2 seconds between the time I push the channel up button and the channel actually changing) my box doesn't have the serial connector so I don't know if that method is faster.
Although I haven't tried it, I don't believe you can record one channel and watch another with this configuration as the channel is being controlled by the cable box and the box can only tune one channel at a time.
Hope this helped.