I'm so sorry you're struggling with this. It's hard to meet your child's needs in the way you know to be best when your spouse isn't supportive. While I in theory like the idea of placing the burden of proof on your husband, I wonder if that's really going to help. It seems more of a communication issue and a difference in parenting beliefs/styles. Have you tried to talk to your husband about this when you are both calm and receptive, using good communication skills and active listening (if you don't know what this means, books such as "Nonviolent Communication" and "How to Talk So Kids WIll Listen" are good resources - the second is not just for kids, it works with husbands too :-). There will be many instances over the years where your beliefs on childrearing and parenting differ. It's so important to be able to talk issues out, come to agreement or at least a point where you can agree to disagree. I'd make sure your husband has really heard your ideas about this - that it is incredibly important to you and your daughter, that you believe that this is the best for her and for you, that you have read a lot about it and believe your decision is supported by research. But it's also important for your husband to feel heard - he's uncomfortable with breastfeeding an older child, he wants to protect his child, he's worried about her.
You might find out that he's getting flack from a friend or co-worker, or from his parents & is taking that out on you. Perhaps he really doesn't understand how important this is to you, and doesn't realize how his comments are hurting. Perhaps he has no experience with "normal" breastfeeding, has never really seen or known anyone who has breastfed, and just doesn't realize that many children nurse beyond infancy.
If you find you cannot discuss this with him productively, you might want to get help from a couple's counselor, pastor, communication skills expert in talking about this issue.
It might also help to spend more time with other families who are parenting in this way. Does he have "dad" friends? You might want to cultivate friendships with others who believe in things like full-term nursing, gentle discipline, and the like so he can see that others are raising their children in similar ways. Even better if he can be around older children and teens raised in this way (he'll probably be pretty impressed, especially if he can compare with older kids raised in less gentle ways). You might also try strewing books and magazines that discuss the science and psychology behind attachment parenting, positive discipline, extended breastfeeding around the house for him to hopefully pick up and read. The back of the toilet is a great place to stack some magazines.