Why does the order of 人口 change?
You're right that 口 is one of the measure words for 人, but 人 (people/person) and 人口 (population) are two different words. The word 人口 is mostly used for the population of a city or a country instead of a household.

You can say 几口人 (how many 'units' of people), 三口人 (three 'units' of people), but not 三口人口 (three 'units' of population).