The concept of the Edge being able to work with multiple bikes, and the gear tracking in Connect, are completely separate. You have to manually enter the gear (bike, anything else) you used in Connect. You can set one bike as your default and it sounds like you've done this with your road bike, so you only have to edit things when you were on the hybrid.
I know it
should be able to do it. But it can't and that's what you have to do if you want the mileage breakdown by bike.
