Lloyds TSB in Jersey is good.

You can have accounts in Sterling, Euro and $US. They have excellent internet banking facilities and Visa Debit and (I think) credit cards. You can access your accounts through any Visa Hole in the Wall.

Of course, to set up accounts you will need to comply with money laundering requirements, but that is the case with any European bank now.

They also have an investment service including proper stock brokers. I should say that I am only connected to them by way of being a customer.