Our baby is 3 months old. We also have a 2 yo who's being assessed for ASD and is up anywhere up to 20 times a night. Our 7 yo sleep walks/talks and has night terrors 4/5 times per week. DP sleeps through all the goings on in the night and wakes up completely oblivious asking if the kids and I slept well.
On Saturday he fell asleep at 9pm, despite not having got up til 10am and slept until 8 yesterday morning. Itook the older two for a bath at 7 last night and when I came down to get something ten mins later he was asleep holding the baby and she wasaasleep with her face squashed into the pillows. Last week I came in just in time to stop her rolling off him when he fell asleep at 8pm.
He has no health problems and would quite happily/easily stay awake if sex was on the agenda so falling asleep with the baby - when he has no reason to be tired - makes me furious. His response last night was to apologise and say he'll give me the baby to take with me to bath the others if he feels tired next time...!