I gave birth naturally to my identical twin boys almost exactly 7 yrs ago!!!
My older daughter was born in a free-standing birth center, quickly and easily at 37 weeks gestation.
I planned a homebirth for my second birth, but found out at 24 weeks gestation that I was carying twins. My homebirth midwife was not comfortable attending twin homebirth, so I transfered care to a CNM at a Baby-friendly hospital. Despite their best efforts to "mainstream" me as "high-risk", I managed to get an agreement to a basically "hands-off" approach. They were willing to do Baby B vaginally if he were breech (he had been bouncing up and down from vertex to footling every other visit!). After having regular u/s and Non-stress tests for a few weeks, I got fed up and stopped having them.
At 37 weeks, my water broke. Contractions started within an hour, and we did the half hour drive to the hospital with my mom and daughter. Dh met us there. My homebirth midwife was my doula, but she missed the birth!
Unfortunately I was required to birth in the OR and I did consent to a hep-lock, but other than that, I was free to labor in my room, move around, get in the tub, drink/eat, etc. (hand-help doppler rather than constant EFM).
Both babies were vertex (yay!) and born 4 hours after I arrived at the hospital. I was zoomed to the OR when I was complete and had the urge to push. Baby A were born less than 20 minutes after I got the OR, then Baby B was born 13 minutes after. They weighed 5-13 and 5-7 (which was more than my single who was 5-7).
We went home less than 24 hours after their birth. Breastfeeding went great and they nursed exclusively until 6 months, and naturally weaned before their 4th birthday (about 6 weeks apart).
The first 2 years were very challenging (although the challenges were frequently changing!)--and it got gradually easier through that time. Now that they are almost 7, it is such fun! We homeschool, and they love having a best buddy around! It's easy to forget that at 18 months, it was constant draining work.
As far as that natural birth of twins, it can totally be done! I am a doula and I was at two twin births last year. They were as different as night and day. Each mother had her own priorities and world-view. One had a quick vaginal hospital birth, the other had a long induction and epidural, with one vaginal birth and one cesarean births. Both were satisfied with their births.
One more thing--if there is one big thing that carrying, birthing, and parenting twins has taught me, it is that we do not have control over many things in our lives. Control is an illusion, for the most part.
Planning every detail of our lives (or birth) is not a productive use of our energies. What is valuable is delving deeply inward to explore our internal resources, as well as gathering external resources. Knowing that you have a bundle of coping skills is what will get you through birth and parenting 2 babies.
Knowing that I cannot control life, but that I CAN deal with whatever comes my way is the greatest gift that my twins have given me.
Feel free to pm me, if you want more info! I am a doula, IBCLC, and childbirth educator.