So for looking at the AC component riding on DC you use AC coupling at the vertical input (blocking the DC level). Then you increase the vertical gain allowing you to see the AC. That is how we look at ripple. Did you ever see the sine wave fro your transformer before the rectification? The scope will display the actual peak to peak value of the sine wave.
You can't view them at the same time, since they do not share a common (the transformer input to the bridge rectifier is floating with respect to the DC output common). To view multiple channels at the same time, they must share a common (ground) connection.
Edit: If you connected one scope probe common to the transformer output and the other probe common to the DC output common at the same time you would likely blow the diode bridge.