I am changing it in the settings tab by clicking the UNITS button to toggle it.
After talking with a few people with knowledge of Mach 3, I think I finally understand what is happening.
When I click REF ALL HOME, it sends a g-code command to move left until the sensor triggers, then sends a command to move right 0.5. If units is set to mm, it moves right 0.5mm. If units is set to inch, it moves right 0.5in.
I also learned that the units setting is simply the native units for the software interface, so there is no need to change that. The toolpaths will generate the codes to set the units for the toolpath.
Therefore, I will be keeping the units on the machine set at mm so that I get an extra 0.5" of cutting area.