As a general principle, it is best to borrow in the currency in which you are going to hold your assets.
Let's say you borrow in € and buy a house in $. You then run a currency risk. If the $ depreciates against the €, you will lose money. But if your borrowings are in $, then the value of the property and the € amount of the loan will decline equally.
Presumably, it's reasonably easy to get a US mortgage of around 90% of the value of the property. But if it's not, then you should get as big a US mortgage as you would be allowed, and release some equity in your home for the balance.
Brendan