I currently drive a 2007 Honda Fit and have plenty of cargo space to put a full size mountain bike or road bike in the back when the rear seats are down, without having to remove the front wheel. In fact, I can carry 2 bikes in the back if I remove the front wheel on one of the bikes.
For my next car, I want to be able do the same thing.
Can the 2016 Mazda 3 hatchback accommodate bikes as mentioned above, or will it be a tight fit?

 

I haven't tried but I'm thinking it would be a stretch to get my mountain bike in the back without taking the front wheel off; two bikes might be an issue as well. The advantage the Fit has is its interior height; while I haven't measured, my eyeball tells me the Fit has a several inch interior height advantage between the floor and the ceiling when compared to the Mazda3.

 

I forgot to mention. When I place 1 or 2 bikes in my Fit, both bikes are lying on their side. They are not upright. So- would one or 2 bikes fit in the Mazda 3 lying on their side? In these instances, the front fork would be turned and the front wheel would face upwards.

 

I don't have two bikes to test, but I fit my touring bike behind the front seats, even with the front wheel mounted. I've got the 5-door.