Most "Internet banks" (i.e. NetBank, American Bank/PC Banker, Umbrella Bank, E*Trade Bank, American Express Bank, State Farm Bank, TD Waterhouse Bank) have a customer lobby where a client could conduct in-person transactions with tellers or bank employees. But these banks do not operate "branches" of that single main office, and so they could be considered "branchless banks" even though they do have a brick-and-mortar main office that offers teller-assisted transactions.

As a practical matter, "brick-and-mortar" refers to an bank that operates multiple full-service teller-staffed banking facilities ("branches" of a main office).

It gets murky when we look at ING Direct which, as I understand, has several "cafes" which provide customer information but offer no actual teller services to customers.