I know you're really tired, but it is fairly common for babies to wake up that often, especially if you are nursing. Breastmilk digests in an hour! Most babies will need middle of the night feedings until abut 6 or 9 months. It really takes a while before a baby can ingest enough during the day that you know they don't need night feedings.
My suggestion is that you start pumping. Find 1 or 2 times in the day to pump for 15-20 minutes with an electric double pump. Wait about 20 or 30 minutes after feeding your babe and then pump. Go to the Medela website for tips on storing/freezing milk.
Have 1 or 2 bottles of milk ready to go in the fridge and have your husband or partner do at least 1 nightfeeding so you can sleep. If your husband is resistant, let him know what hell your life is, which translates into HELL for him, if he does not agree to be a dutiful husband.
Your body will adjust to the pumping. The first few days, you may only get half an ounce. After 3-5 days, you'll be getting as much as a typical feeding.
This is what I did, and I can honestly say it saved my sanity!! Was it tough on my husband? Maybe. But he got used to it and I was a much more agreeable wife because he helped in this way.
If you are not nursing, then so much the easier!!! Just make your husband do the night feeding of formula! You're already set to go.
If you are a single mommy, then try to learn nursing lying down...
BTW - even if you decide to cry it out to train your babe to sleep (we did), sleeping through the night is defined as 6-8 hours, so you still might not get the sleep you want or expect. Remember, 6 hours is considered through the night!!
Anyway, if the whole pumping thing sounds confusing to you, I would seek out the lactation services of a local hospital. Maternal Connections is the place at El Camino Hospital in Mountain View. They do free phone consultations and the ladies are very knowledgeable. I think I read some useful things on www.kellymom.com and the la leche league site too.