adrienn Please make sure to separate your bank account and your card. They're two different things. You deposit and withdraw money to/from your bank account at bunq, and you can use any of your bunq cards to spend it. The cards are solely tools that can be used to spend money, they do not hold money on their own.
But now onto your inquiry: You said that the IBAN of your bank account wasn't usable in some situation while being in Italy. Could you further specify what you have been trying to do? Did someone attempt to send a bank transfer from an Italian bank to your account at bunq? Did you try to put your bunq card into an ATM and deposit cash? There are many different scenarios that I could think of. Please describe exactly what you're trying to do and what you want to accomplish. Then we might be able to help you further.
If you want to deposit cash to a bunq account in Italy, that's actually very easy: You just need to use Viacash at any of the partner stores. Read this article for more info: https://together.bunq.com/d/14531 Please do not try to use your card at an ATM for cash deposits. ATMs can only be used for withdrawals.