As a few people have mentioned on this thread - plenty of ("real") companies (and even the "real" jobs in theatre companies) offer maternity leave but no pay. I think this is, while not the greatest, perfectly fair. Having a baby is - on the whole - a choice. The same way taking a vacation would be a choice. And not all companies offer automatic paid vacation either. The biggest thing in maternity leave is a guarantee that you will have your job back in 6 weeks, 8 weeks, whatever the maternity leave allows for. Just like an employer guarantees not to give your job away while you're on a vacation.
As a freelance contract employee, there is no guarantee you will have a job, ever, after the current contract you're on, so AEA can't really offer a maternity leave option. How would they? Right now I have a total of 2 contracts lined up through end of next May. I could time it to try to get pregnant sometime in November and it would work out about perfectly to have a baby after those contracts are done (now...I'm just ignoring the fact that stage managing a show at 7 months pregnant might not be the most fun thing in the world - but is any job?). And then it's up to me not to take any more work that would conflict with having my baby and how long I want to stay home after that. I can't call AEA and say, "hey, I'm having a baby in June, but I really want to start working again in August, so I'm calling in my maternity leave and can you make sure I have a contract by then? Thanks."
I'm not having a baby right now, but I AM going on a tour to the Dominican Republic at the end of November with a dance company. It's throwing a huge monkey wrench in trying to book an equity contract between the one I'm on now and the one that starts mid-January - but that's my choice. I want to do the tour - so that means I need to plan for essentially 4 months of unemployment (the tour is paying me about...1 peanut). But, it's important to me artistically, so I'm going to find a way to make it work.
On the whole, in a freelance situation, having a baby is no different than a choice like that.
I think you have a little bit of a different situation because you have a resident position - if I were in your position, I would go straight to your director and to HR (or whoever the HR equivalent would be) and rely on the good relationship you have with them - since your AEA contract offers no provision for you. Think of what you absolutely need in terms of having a baby - you want 10 weeks off and then want to come back to work. I agree with other folks here - you need to be able to do those 10 weeks without pay (since, as we've already mentioned, that's most other real jobs as well, especially non-profit jobs), but they should guarantee your job at the end of those 10 weeks. What is the policy for the other, non equity employees in the company? Appeal to that.
I think the larger issue with our union here is INSURANCE. If by having a baby you preclude yourself from being able to get your 20 weeks - then all of a sudden you've lost your insurance at the time when you need it most.
THAT is a problem that our union COULD fix by offering provisions for women who get pregnant and so for whatever reason won't be able to get their 20 weeks. They don't have to let this go on indefinitely - it could be a "you get to keep your insurance for one year after having your baby regardless of work weeks, and then after that you go back to the work week standard" or something similar.
Balletdork, I don't know if this is an issue for you - maybe you're on your husband's insurance policy, but plenty of women out there are having babies without husbands or a partner who's insurance plan they can just jump onto.
Those are my thoughts for right now. Maybe if I were the one having the baby though I would feel differently. Hard to say.