^^
Taken from the H3 2006 Owners Manual
http://www.hummeranswers.com/files/hum_h3_2006_man.pdf
If the system is ever reset accidentally, you must
change your oil at 3,000 miles (5 000 km) since your
last oil change. Remember to reset the oil life system
whenever the oil is changed.
There is no specific line in the manual that I can find, but I do see that they indicate 3K and my dealer always adds 3K to my current mileage for my next oil change. So what have you got that is different?