My son went thru this - it's so frustrating. No one's getting any quality sleep. We had a great experience with our pediatrician, and with the pediatric urologist to whom she referred us.
The condition is call nocturnal enuresis, which means peeing at night. It's a purely developmental issue - the signal from the bladder to the brain that says "I'm full" simply doesn't get there in a strong-enough message to wake the child up. It's much more common in boys, but girls get it too.
You probably have heard the horror stories of kids being humiliated over this 20 years ago - parents punishing them, hanging the sheets out the window for all to see, etc. There is simply nothing you can do to "TRAIN" the child - it's much more like learning to walk, getting teeth, learning to speak -- it occurs on a different developmental schedule in each child. Every child who isn't doing something yet in Area "A" is doing other phenomenal things in Area "B" - it is so important to realize that.
Once my son realized that it wasn't his fault, he was fine. There are new products now that are a little more grown-up looking than a pull up and which will hold greater quantities of urine - that's important as the child gets older and produces more. They even advertise them on tv - something about fitting under pajamas without the bulk of a regular pull up and I think without the juvenile designs.
In the short run, you can consider making the bed with 2 sets of bottom sheets - I put down one sheet, then put on a waterproof pad the size of a crib mattress but not fitted - it's big enough to cover the area where his abdomen was, and it didn't matter if his head or feet weren't on it - and then I added another sheet. If things go wet, I wiped him down with bathroom wipes (the ones we all use, not the baby ones), pulled off the sheet and the pad, and left him with a dry sheet.
I'm not a big believer in medication if it can be avoided, BUT there is a drug made for this exact purpose, and it had no side effects whatsoever. The pedi urologist told us he has some kids on it well into their teens. My son took it until age 9, went off it and the problem returned, and he went back on until around 11 or 12, when he took himself off. He never had a side effect, and when his body had fully developed, everything worked right.
The result was, he (and we) got a full night's sleep every night, he went to sleepovers, and he even went to overnight camp at age 10. He took one pill at night - for sleepovers, I sent a single pill to friends' houses in a plain unmarked bottle and told the other mom to make sure he took it. They thought it was an allergy pill and no one asked a single question or looked at him funny! At camp, obviously I sent a supply in a marked bottle, and the camp nurse gave it to him every night. Kids are on so many meds these days, no other kids even comment on it.
Prior to this, we tried waking him up at 11 to pee, cutting back on liquids, and even using those alarm systems that hook to their underwear and wake them up at the first sign of wetness. Looking back, it was a waste of time, and the alarms were barbaric - we still had wet sheets and a midnight awakening, but there was this huge buzzer going off too! None of it worked.
Good luck with this!