Hi fellow mummy! Yes it's perfectly normal.
Well, i am a mother of two now, i really don't know what is sleep now. Been sleep depreived for so long. Give your baby some more months, soon they will be able to sleep more and longer during the night thus you will be able to feel more rested.
Hang in there
P.S - It's pretty common for husband to be like this. They don't know how tiring it is looking after children
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