Pick up the thread of that conversation you began. Do not wait. Time will elapse and it will be harder to bring it up again with him. You and he together should go to a parenting class or counseling pronto. Find some classes or family counselors and then sit him down at a good time (kids not around, he's calm) and let him see that this is important to you.
It should be important to him because his children are already starting to think of him as "cranky dad" and "yelling dad." Tell him that it breaks your heart to know your children already associate him with anger and raised voices, not with affection and calm. Is that how he wants them to identify him and remember him?
You can tell a kid a thousand times, "I really do love you and you know I'm not really angry when I yell...." but the thousand times mean nothing against the times he does indeed yell.
Their teenage years will be a nightmare if he cannot learn before then to be more flexible, pick his battles and choose to praise them rather than criticize. By then they will not want to share anything with him for fear they won't meet his high standards and will just get yelled at. Is that how he wants them to see him?
No, of course not. But can you get him to see that he's on that path?
If he pulls the "my dad yelled at me and I turned out OK" routine that some people use -- oh, truly, parenting classes/counseling are truly vital.