BMO IL has a feature called something like 'Link Account' or 'MyLink' or something like that which could have been opened at the same time as the BMO IL account(s), and allows those that otherwise do not bank at BMO to use it as a chequing account ( 1-2 free transactions a month). It has a bank transit number, etc. and provides all the features of a chequing account (Interac, Bill Payments, Transfers, etc.) It "holds" the balance of cash from your BMO IL account so that you can use it like the balance of a chequing account. You might be able to still set that up simply by calling BMO IL (avoid anyone at the BMO bank branches as they have little idea how anything works with BMO IL). You can also set up a USD bank account with Harris Bank in the USA, owned by BMO, and that will show up on your online banking. I liike those features from BMO IL.
BMO IL is a good discount brokerage in my opinion but it still is a little behind in some things. It does not yet issue online PDF tax documents, does not offer IPOs, and does not yet have an integrated BMO IL and BMO Banking online page (all of which I get with Scotia iTrade).
Added: As previously stated, all the big banks/brokers have trouble dealing with out-of-country individuals.