what should I expect

I have a longer guide on my site below on breaking into finance from engineering, but the #1 thing they will ask you is why you want to go from a 40-hour a week job at Google/Yahoo/Microsoft to 100 hours a week at a bank and not get paid that much more (at least, on a per hour basis). You will also be asked about your ability to handle the stress of the job which is way more than what you'd find in engineering positions.

Ways to answer: yes, going to a traditional company is cushier in the short-term but in the long-term you're more interested in business and banking can take you very far, feel like you're actually doing something that affects what's going on in the world unlike a normal company where you just build a product, etc., anything along those lines.

For ability to handle hours/stress just cite a couple times where you pulled all-nighters working on projects or spent a good portion of a semester locked up in a the lab or something.

I would also suggest spinning your internships into experience that looks like leadership or something more business-oriented.