Ruling on buying halaal shares through riba-based banks

It is permissible to buy shares in permissible companies via
the banks, and what the riba-based banks charge from the purchaser or
company is only in return for serving as an intermediary, and it is a fee
that is permissible for them, because it is in return for permissible work. 

Shaykh al-‘Uthaymeen (may Allaah have mercy on him) said: 

There is nothing wrong with dealing with the banks in
permissible transactions, for example, I may buy from them, or get change
from them, or transfer money through them – there is nothing wrong with
that. Rather what is forbidden is riba. If it is not riba there is nothing
wrong with it. It was proven that the Prophet (peace and blessings of
Allaah be upon him) bought from the Jews, and accepted gifts from them,
although they consumed haraam wealth and took riba, and when he (peace
and blessings of Allaah be upon him) died, his shield was being held in
pledge by a Jew. 

Liqaa’aat al-Baab il-Maftoohah
(70/question no. 7) 

And Allaah knows best.