All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
If these branches of banks that deal with Riba (usury and/or interest) do not deal in any of their transactions with usury or interest as their owners claim, then it is permissible to deal with them according to the Sharee'ah. Dealing with these branches in such a case is like dealing with a person who usually deals with usury and interest in other transactions that are lawful [free from usury and interest].
It is permissible in Islam to deal with people who deal with usury and interest in lawful and permissible transactions as the Prophet used to deal with the Jews who dealt with usury and interest. Indeed, 'Aa'ishah narrated that the Prophet died and his shield was kept as a deposit with a Jew for 30 Saa' (i.e. a measure of weight) of barley.
However, one should make sure that this claim is true, that there is really a religious committee who runs these branches according to Islamic principles. That is because many banks claim that they are Islamic banks whereas in reality they are otherwise. A bank that deals with usury and interest is subject to accusation, therefore one should not believe their claim of having Islamic branches; rather one has to investigate whether or not their claim is true.
Allaah Knows best.