There are some good reasons why they couldn't use "normal money".

The payment of active duty soldiers on occupation duty presents some interesting macroeconomic problems. If the soldiers are paid in their local home currency (say pounds or dollars), then they represent a constant infusion of hard currency, which runs the risk of devaluing the local currency (say, marks or francs), as the dollars are more valuable than the local currency, especially since dollars can be used to purchase expensive imported goods. Thus the payment of occupation forces with their home currency risks creating an inflationary cycle that undermines efforts to stabilize and rebuild the (presumably devastated by war) local economies. Additionally, the high purchasing power of the currency of the occupier creates opportunities for black markets and also for money laundering by criminal elements.

However, the opposite solution, of paying occupation forces in true local currency, has some other problems -- soldiers don't like being paid in money that has less purchasing power back home, and printing more local currency to pay the soldiers wages at purchasing power parity virtually guarantees the rapid devaluation of the local currency with all the problematic economic effects that planners are trying to avoid. The real-world macroeconomic feedback cycles are a bit more complicated than I am describing, but this is /r/AskHistorians, not /r/AskEconomics.

The solution that mid-20th century economists devised is to pay the soldiers in special banknotes issued by the military, called military payment certificates or "army banknotes", whose supply is carefully monitored by the relevant officers, and whose conversion to regular home currency can be strictly controlled by the military supply chain, with the cooperation of the central bank (or it's equivalent) of the home country of the occupying army. The United States stopped issuing military banknotes sometime in the 1970s, by which point the only country they were still useful in was South Korea, which by that time had a strong enough local currency that American troops could simply be paid in ordinary greenbacks without posing a danger to the local economy.

I knew that both the United States military and the British Armed Forces issued their own respective military banknotes or payment certificates. However, I did not know that Denmark issued it's own occupation currency -- would you be willing to post a picture of it?