My B/G twins were born at 29 weeks and have finally come home after 7 weeks in the NICU; however, I don't want to leave them alone for a minute and I'm terrified something will happen if I sleep....my reflux girl will spit up and choke, my boy will have an apnea spell, etc. (not on a monitor). Is this normal?

Re: Terrified to go to sleep now that preemies are home??
Andrew was a 26-weeker and while I wasn't that afraid of those things, he did have some reflux troubles. We kept the monitor on and we could hear him if he had trouble.
I think in general, worrying is normal. I hope that you are able to get some help for a couple of weeks!
Hugs and prayers that your first weeks go smoothly!!
I think it's normal even if your baby isn't a preemie- they just seem so frail outside of the relative safety of the hospital.
It will die down but I don't think it ever goes away. DD is 15 months and I still have nights where I'm just compelled to check on her. DH has stopped harassing me about it- I figure I've got about 18 more years of it.
I say it's ok to worry- indulging your fears a little bit will keep them from being blown into full on paranoia. If you feel better having them near, do it. If you want to set an alarm to check them every two hours, do it. Give yourself some time to adjust to life at home with LOs. Don't lose too much sleep over it, but do what you need to do (within reason) to start building up your confidence away from the watchful eye of the NICU.
FWIW- we bought DD a hard sided co-sleeper to keep her near by. A blackberry alarm is quiet enough to not wake them and lets off just enough light that you can check on them and then head back to sleep without disturbing them!
The video monitor is your friend. Corri is 8 months old and has been home from the NICU for 6 months and I STILL jolt awake several times a night and check her on the monitor to make sure she's ok. The video monitor is a lifesaver because I can see her rather than just hear her. An Anglecare monitor may not be a bad idea either, but be warned that there are false alarms, which would drive me insane.
What you are feeling is totally normal...my whole family thinks I am nuts for this constant checking of the monitor but honestly, the NICU scared the heck out of us with regard to SIDS and until she is at least a year old I am going to be "that" crazy mama, lol!