Two thoughts:
(1) What version of Mach4 are you running? The default screen set in some of the earlier versions had the "Ref All Home" button programmed to only home the X & Y axis. Newer versions fixed this - It looks like version 2336 and newer have fixed this (I don't have any older versions installed to check so I don't know exactly which version fixed this, I checked 2336, 2471, 2492 and 2580).
(2) How do you have homing configured for the Z axis? Go to the "Configure" menu and select "Mach". In the configuration dialog, click on the 'Homing/Soft Limits' tab. The "Home Order" must be non-zero in order for Mach4 to attempt to home that axis (i.e. "1" is the first axis to be homed, "2" is the 2nd, etc.). Also, the "Home In Place" column must have a red "X" in it (home in place means don't move the motor, just declare its current position as "home").
Bob