The actual name of the type of account does not matter, but it is a joint account requiring signatures of the two account holders. While opening the account, make sure that the bank understands this. (This account would be different from many joint accounts that require only one of the account holders to sign).
Two-signature required .This could be a business account or in theory a personal bank account. These days I doubt you will find a bank that will open a personal account with two signatures required (but you might at some small bank that does their own processing -- just very few of these exist).You might have a hard time finding a business bank account with two signatures required. If you do find one, check the terms very closely to see if it is actually required or just for your convenience .This type of accounts definitely exist, you just might have to ask around a little bit.