The good news is that you will only ever pay a single monthly fee - even if you choose to operate two Monese banking accounts. The currency of 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.
A UK primary account: Costing a monthly fee of £4.95, no additional fee for EUR account
A Eurozone primary account: Costing a monthly fee of €4.95, no additional fee for UK account
Free ATM withdrawals are shared between the accounts (6 per month) and consequent withdrawals are charged £1/1€ respective of which card was used.