I think it's insane. Not because it will be too hard, but because it will take way to long (very little course overlap). You'd probably be looking at upwards of 6 years without internships/co-ops so that you could have two degrees in different fields that aren't particularly complementary. Odds are, you'll end up working in one field or the other, and will be no more competitive for either field. BME is a little bit difficult to break into without a graduate degree. In 6 years, you could have a master's in BME and be much more qualified for a BME job. If you take the CS route, you could have 2 extra years of income and experience at the start of your career, or a graduate degree (which is less important in CS).
It's really not a good idea. If you want to double major simply because you are interested in both fields, that's not a good enough reason. You can be interested in one and read about it in your spare time if you like.