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He has been physical with me in the past, but I insist that he is not that kind of person.

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The fact that he has hit you in the past suggests that he is that kind of person. Why should he change?

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I need to see the best in him, but I am afraid.

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If he was a good, kind man, his good aspects should be immediately apparent. You shouldn't have to search for them.

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he had reached into our chihuahua's cage, I don't know for what, but the dog bit him.

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Often when dogs are in such places, if somebody reaches in they bite or nip. After all they are cornered in there and there is no way out and if somebody starts reaching in, they don't know what the hand will do and they will feel threatened.

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Immediately I realized that Jon would erupt if I locked the door, so I unlocked it.

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Does that mean you were afraid he would turn his anger on you?

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he began to scream at me for disrespecting him.

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To me, that sounds extremely controlling. I wouldn't say most people see an attempt at stopping somebody from hurting a small dog as 'disrespectful.'

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he is still upset with me today, and is berating me for all sorts of things- as he usually does.

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From the sound of it, he is taking his anger out on you. You shouldn't have to live with him constantly yelling and nagging at you all the time.

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He is usually such a nice person, and I love and care for him.

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Don't excuse him. He'e been violent towards you in the past, and he could easily have killed your dog the other night, either by snapping its neck when he held it by the throat, or breaking its bones when he threw the dog into the yard. Maybe he is ordinarily a nice person, but this streak of anger and violence he has makes him dangerous.

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I can handle his abuse on me

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You shouldn't have to put up with it.

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I am not going to quit something I have worked on.

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Does that mean you're trying to convert him into being a nice caring guy who never hits you or the dogs? If you are, it'll never work. That nasty side to him will never change. Besides, you'll always be afraid that he will erupt again. And unless your chihuahua is extraordinarily forgiving, he too will be afraid of your guy, and may bite him again if he feels threatened again, which may lead to a repeat of the other night.

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me leaving would destroy my will to do anything.

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Why?

So I agree with the others, in that you should at the very least see a counsellor about this, and if possible move out asap. I know you say you don't want to move out, but he is certainly not stable, and since you say he is drinking a lot there is a high possibility that the situation will worsen. The fact that he has used violence against you before does not mean he won't do it again. You shouldn't have to live in a place where you are scared for yourself and for your pets, and frightened of his anger. You don't deserve it.