Thank you for contacting the tax experts at Justanswer.com!
You pose an interesting question, for which the answer hopfully is not too hard to understand. Basically, interest income from foreign banks is treated the same way as though you have received them from a domestic (U.S.) bank. The practical difference is that you would not receive a form 1099-INT which shows the interest income received for the year which you would have gotten from an American bank.
Now, there are several provisions in place that would prevent you from paying tax twice on the same income, in your case on interest income. If your account is located in European country that charges tax on the interest income (vs the value, the balance of the account that some European countries tax) then this foreign tax paid could be used to calculate the foreign tax credit on your U.S. tax return. In other words, the foreign interest income will be taxed in the U.S. at same rates as your domestic interest income, but you can offset the U.S. tax calculated on the foreign bank interest by the tax you paid to the European country. Keep in mind that even though the foreign tax credit reduces your U.S. tax liability dollar for dollar, there are various limitation and calculation made to the foreign tax paid before you can apply it in that manner. If you plan on using this set-up, I would advise to use a tax professional to prepare your 1040, especially is you are talking about a significant amount of interest income. The reason I say this is because there is a lot to the calculation of the foreign tax credit and it takes somebody with experience to get it right.
If you would like to know what the general tax rates are in U.S., please refer to this IRS publication:i1040tt.pdf. Simply visit irs.gov and type "tax table" into the search box and it will be the first at the result list.
Again, keep in mind that there is no special tax treatment for foreign bank interest received by a U.S. taxpayer and that this income is treated like ordinary income. But the foreign tax credit, in most cases, does prevent double taxation of the same income.
If you have more questions, please let me know! I aim to please.