How would you express currency that has over 2 decimals? For example if you said €65.37 that would be "sixty five euros and thirty seven cents". If you have €65.375 would you say "sixty five euros and three hundred seventy five cents". I guess that is wrong though since "three hundred seventy five cents" is actually €3.75
I would read
€65.375 aloud as "sixty-five euros, thirty-seven cents and five tenths of a cent".
It is hard to find authoritative references in writing for how a figure should be read. But it is an established form when writing sums in legal documents - for example:
... there shall be paid unto the said Matthew and Peter, or either of them, the sum of one cent and seven-tenths of a cent per page for each and every page of said work so printed and published by them or either of them, ...
Report Made to the Hon. John Forsyth, Secretary of State of the United States ...
the gold coins of Croat Britain, Portugal, and Brazil, of not less than twenty-two carats fine, at the rate of ninety- four cents and eight tenths of a cent per pennyweight ;
A Dictionary Practical, Theoretical and Historical of Commerce and ...
You can also say sixty five euros and thirty seven point five, or thirty seven and a half, cents. In general, the value is just a number. You can say sixty five point three seven five euros, or six thousand five hundred and thirty seven and a half cents. If you always want the number of cents to be less than 100, and the number of euros an integer, then for example 65.76543 euros is sixty five euros and seventy six point five four three cents.
You can also say it any way you would express a fractional number. You could say seventy six and five hundred and forty three thousandths of a cent, etc.
There used to be a country whose currency actually did have three decimal places: Cyprus.
After decimalisation of the Cyprus Pound in 1955, it was divided into 1000 mils. (This was simplified in 1983 to 100 cents before Cyprus joined the euro in 2008.) £3.456 was read as "Three pounds, four hundred and fifty-six mils".
The only other currency I know of where there were subdivisions of a "cent" is the Pound Sterling, where prior to 1971 a penny was subdivided into four farthings and from 1971 to 1984 into two halfpennies. However those fractions were actually represented as fractions like ¾ and ½, and were read as "x pence three-farthing" or "x-and-a-half pence".