Welcome to the board Yorkie,
It always puts a smile on my face when I see couples work through their anxiety issues. You are very supportive of him and you sound like you and him are both good parents for your children.
Anxiety takes over emotion like the plague. It's a horrible sense. Nothing is worse than fighting mental battles constantly. Especially when you never know where it has rooted from. From the sounds of it he is built up with this own battle (yelling at the kids) but that is his anxiety showing through. To hear that he is not aggressive towards them shows that he has a handle on himself, even if it's a loosening grip.
Being that you were there for him through all of his health fears shows you as a great companion. Those with anxiety have a hard time expressing or talking about it because people will look at them as if they are overracting... often being told "just don't think that way, or just knock it off". We are all entitled to our own feelings and we all have Anxiety... it's what keeps us alive. some of us just have a little bit too much juice in the blender.
I am glad that he is looking into Therapy... I remember the first time I stepped out of the office of therapy just for introduction purposes, I felt like I had a handle on my life... for the first time in 5-6 years. There he will learn how techniques to view things from a different perspective and fight through this struggle.
You mentioned he started on Zoloft. I am as well... I'm on my 5-6-7th day of it (I can't keep track) and believe me it gets worse before it gets better... I've had the worst anxiety this week than I have had since this anxiety manifested. Sometimes the psych will give you something to calm these anxiety spikes but they are to be expected.
Not everyone experiences them but they do happen. I haven't had much of physical symptoms other than being pretty sluggish, but it will all go away eventually. Stick it out.
Welcome to the board, post around... with anything. we're judgement free here.