Last night I started an argument with my husband which led us to leave a movie that just started. We were both talking in very loud voices and a woman butted in and threatened to call the police if my husband didn't stop yelling at me. I was already in tears and I didn't do a thing. I didn't tell the woman to mind her own business or tell her that I was fine or anything.
Nothing like that had ever happened before to me and I didn't know how to react. I couldn't process what had just happened. I feel like a horrible wife. My husband feels like I didn't have his back - that I didn't stick up for him. I feel terrible. Something like that would have really meant something to him and also make him feel a tad better (I think he's going through a depression).
I feel terrible for the timing of my argument. I feel terrible that I didn't have my husband's back in that moment. And I just wish I could help him with his depression.
He says everything is a disappointment - his job, his family, he has no friends, his hobby, and me.

I've been depressed before. Or rather, I've felt the way that he has felt, but I don't know what I'd want him to do for me. I want to be a good wife and I want to be his best friend. I think my not defending him made him feel like he doesn't have a friend in me either.

What do I do? What can I say that could make him feel better?

Stick up for him? He was yelling at you in such a manner that it was considered abusive by a third party and you think you should have stuck up for him?

It really wasn't as loud or as abusive to warrant a woman to butt in. We were both communicating the same way.

You said if your husband didn't stop yelling at you she was going to call the Police.

That doesn't sound like the third party thought you were "communicating" in the same way.

This was spousal abuse. I don't know why you are excusing him.

You and your husband have had problems in the past. He apparently is jealous. You apparently lie/lied to him. https://www.askmehelpdesk.com/marriage/jealous-husband-563490.html

He tells you he's unhappy in all areas of his life, your marriage included.

You both need professional intervention.

Honestly, it wasn't like that. We were walking and waited for the light to change so we could cross and this woman was just standing there by the light. Maybe she didn't see the two sides because my husband was talking when we neared her.

You are not responsible for your husband's actions. Apparently you and he were creating a disturbance and he was being verbally abusive enough that she felt something needed to be said, at least tell you two to take your argument outside.
Have his back? What were you supposed to do, Tell the lady it is all your fault?
If your husband is depressed he needs to go to a physician, you cannot treat his depression by conceding or being passive with him.
You want to be his friend, talk to him about seeing a doctor.

I think your husband has problems and he has you convinced you are the cause of his problems. You two need some counseling before he breaks you down.

I don't think that I'm the cause to all his problems. I feel for him and what he's going through. How can depression not affect every area of one's life? I just wish I could get him to seek help. He started taking exercise classes and it seemed to really help. He was interested in it and seemed to love it because it was a good getaway from everything. Then someone there recognized him (for his work) and now he doesn't feel like it's the getaway it was before.

I just sensed a certain amount of guilt. I don't understand why you felt you should have had his back. If he needs help and refuses to get it, there is nothing you can do.

Both of you need to stop making excuses. Don't enable him by excusing his behavior and not making him responsible for it.

The argument lasted through how many settings (theater and street are two) and getting thrown out of the theater before the woman stepped in? That is more than just raised voices or a brief disagreement. I would have thought that getting asked to leave the theater would have been embarrassing enough tone down the fight if not stop it.

You need to ask him to see a doctor. Many times depression has a physical cause that can be helped with proper rest, diet and exercise, but needs medications too.

Okay so someone knew him at that gym. There are other gyms and ways to exercise. Some might even suit him better than where he was working out if he gives them a chance.

I fully agree with the need for individual counseling and marriage counseling that you can both learn how to communicate with each other and set acceptable boundaries.