On the back of your card, is there a logo for either PLUS or Cirrus? If so you are fine, it's not BOA that is the network, it's the Cirrus (or Plus) network, and these are almost universal in Europe ATMs. BOA can still charge a fee for ATM usage based on their rules on your account, but meanwhile there are no fees charged by bank-owned ATMs in Europe. I am thinking you may find this logo, as we just opened a BOA Mastercard and it shows Cirrus - yes, I know, that's a credit card and not a debit card, and you should never get cash from an ATM with a credit card as this is a cash advance and not a purchase, but this makes me think you may find this on your debit card. CapitalOne is another place that has accounts with no fees at their end for ATM usage, along with Schwab. They are both easy to set up,, but you probably need a month's lead time to get the account, make a transfer, and get the cards.
You are aware that your 3 countries all use different currencies?