A neighbor's dog came into my yard and attacked our dog. We yelled at him to come get the dog, and he said: "If you touch my dog, I'll kill you." I grabbed his dog and pulled it away; then the neighbor attacked me, causing serious injury. Does his homeowner's insurance cover my injuries? The dog also bit my wife.
In the interests of maintaining peace and civility in the neighborhood and of hanging onto your hide, you will want to try to eliminate the shouting, biting, and attacking that is going on. If you do not have one now, consider building a tasteful fence.
Insurance policies, as a rule, do not cover intentional criminal acts. So the neighbor's homeowners' policy probably does not cover his assault on you. The policy may, however, cover the injuries from the dog bite.
Even without the prospect of insurance policy money, you could still sue the neighbor; he may have other assets that could be used to pay you if you win.
You may also want to press criminal charges.