The good news is that you will only ever pay a single monthly fee - even if you choose to operate two Monese banking accounts. This fee is dependent on which is your primary account (whichever one you created first) and is usually collected from that account each month. If there isn't enough money in your primarily account to pay your monthly fee, funds will be pulled from your secondary account to cover it.
Free global ATM withdrawals are available only on your main account.
This allows for either:
A UK primary account: Costing a monthly fee of £4.95, no additional fee for EUR account, 5 free ATM withdrawals on the UK GBP card and no free ATM withdrawals on the EUR card.
A EUR primary account: Costing a monthly fee of €5.90, no additional fee for UK account, 3 free ATM withdrawals on the EUR card and no free ATM withdrawals on the UK GBP card.