In freestyle, coordinating the breath with alternating arm movements and the fact that the breathing action itself makes it a real challenge to maintain balance and Front Quadrant stroke timing (the slight overlap between the arms that helps you "Swim Taller") can be a source of frustration even for experienced swimmers, let alone for novices. So let's eavesdrop on the discussion (a condensed version) and then I'll add further suggestions for seamless breathing.
Rich Kucera: "I don't breathe. I swim the length without a breath. If I have to breathe I have to roll all the way to sweet spot before enough water clears so I can get a breath."

Bob McAdams: "Unfortunately, many swimmers who are balanced most of the time tend to lose their balance when the time comes to breathe, because they lift their heads slightly as they breathe. The point is that if you are rolling your body enough, you should be able to breathe without lifting your head. You probably won't need to think explicitly about hiding your head, because your head will already be "hidden". The point is to roll toward the air instead of lifting your head to breathe."

Rich Kucera: "The breathing problem is fixed. The sensory cue I used was "chin glued to right shoulder for one length, chin glued to left shoulder for one length.The problem was fixed on the first practice lap of the drill. I then could choose to breathe two on one side and two on the other. There is more freedom now to vary the stroke rate, or to hang there in sweet spot, and the cue works without fail."

Bob Wiskera: "When I focused on keeping my ear pressed closer against my shoulder(one lap), presto... I started riding higher in the water. Then I focused on leaning on my lungs a bit more(one lap) and my feet came up, I was horizontal in the water and I rolled right to air."
My two cents: I tried the "chin-glued-to-shoulder" cue for a few lengths this morning and it definitely has the potential to reinforce the most important skills we teach about freestyle breathing.
1. To keep your head aligned with the spine at all times.
2. To breathe with body roll, not as an independent movement of the head.
It's really helpful to use many different sensory cues to help swimmers understand important parts of the stroke. One cue may strike a chord for one swimmer, while another cue may be just the ticket for another. What I liked about Rich's process was that he identified the problem clearly and used curiosity and creative thinking in solving it. Bob M and Bob W also offered advice that was right on the money. This is exactly the spirit of "inquisitive practice" we hope to encourage in all swimmers.
Here are some more sensory cues, excerpted from Triathlon Swimming Made Easy for making rhythmic breathing easier and smoother.

First: Get your head in line.
Lead with the top of your head, not your forehead. Imagine that your head spine line points at the far end of the pool right at the waterline.
Feel water flowing over the back of your head much of the time.
See the bottom directly under you, and not much that's forward of you.

Second: Swim balanced.
Lean on your chest until your hips and legs feel light.
Rhythmically press in one armpit, then the other.
Feel completely supported by the water.

Third: Breathe with Body Roll.
Breathe by rolling your body to where the air is then immediately back in the other direction.
Keep your head in line with your spine as you roll to the air. Imagine that head-spine line as being like a skewer. Roll on that skewer to breathe.
To reinforce this, imagine you'll breathe with your belly button; your head just goes along for the ride.

And finally, see if Rich's sensory cue helps you - keep your chin (or jaw) glued to one shoulder, both while breathing and between breaths.