In our house, I'm the one with less patience than my husband. I'm working on it for sure, but I've got a ways to go before I match his sense of calm. Even so, he's amazingly non-judgmental and supportive of me. Always. Here's what he does to help me stay calm:
First, he never (and I mean NEVER) corrects or criticizes me in front of the kids, even when I'm losing my cool. He just gracefully steps in so I can take a break and clear my head. Often there's eye contact between us in that moment, and it's light and kind -- rolling his eyes about DD or otherwise acknowleging she's being difficult, or motioning with his eyes for me to leave the room, but with a smile on his face. I walk away feeling grateful for the help/support, not embarassed or defensive.
Sometimes he mentions it later in a gentle, non-critical way -- long after the moment, usually when the kids are asleep and he and I are relaxed and happy. He never uses "you" statements (as in "You lost your cool in there with DD.") -- he focuses more on DD and what works with her ("DD seems to calm down more quickly when we do X" and "Remember when you tried Y and it worked?") I come away feeling two things: (1) reminded that DH loves me no matter what; and (2) motivated to do "better" with DD.
I share all this because you're the most important thing that can help DH keep his cool. Shame is NOT a motivator for most people. Neither is judgment. It usually brings out a defensive response -- like what your DH said back to you.
Beyond that, here are some strategies that work for me:
(1) Taking three deep breaths before responding to DD's escalating screaming/fits/demands. I now do it quite visibly -- trying to model to DD so she learns how to stay calm, too. Sometimes I even hold up my fingers to count, one at a time as I breathe.
(2) Imagine I'm being videotaped and everyone I know will gather later to watch the movie. And then it will be played again at my daughter's 13th birthday party, right as she's gearing up for the teenage years.

Silly, but it reminds me not to say or do anything I would be embarassed about later.
(3) Remind myself that DD is learning from my example. If I scream or belittle or otherwise behave poorly, she'll dish it right back at us AND her peers over time. Not good.
(4) I ask DH to step in. Sometimes it's explicit -- "I can't deal. Can you handle this?" -- sometimes it's just walking out of the room for a few minutes and then coming back in. It's ok to "admit" I need a break. I love our kids, but they can be a handful at times.
Good luck.