My other two never did this. They would cry if they woke up or lovingly slap tap my face to wake me up. DS3 is 9mo and when he wakes up in the morning about half the time he's just off causing trouble - standing holding onto the side of the bedside cot (it is tall enough) or I wake up to find him happily chewing my phone with no idea how long he's been doing it. Eek!
I think it might be time to stop co-sleeping. Have your babies done this and what did you do? We are going away soon and will be using the travel cot then so I'll try that out.