Dad and daughter communication

My husband and our eldest daughter (13yo) do not get along. They used to be best buddies when she was little but as she has gotten older and the hormones started flowing, he no longer understands her way of thinking or doing and distrusts everything about her. There have been lies in the past about homework and she tends to not answer her phone with friends sometimes. She grimes about doing her daily chores but still does them (what teen doesn’t imo?!).
Their communication is completely shot at this point. He tries to talk to her but it always ends in angry questioning from him and not believing anything she says which results in her recoiling into her shell. Every time! My daughter and I have a great relationship and it makes it hard for me to not put myself in the middle. I’ve suggested counseling and he’s not interested. I’ve suggested taking note from how I react and deal with those especially hormonal days and he’s not interested. He’s a very old school dad, raised by old school ‘strap on the bum’ and ‘my way or the highway’ parents. So was I but I’ve learnt better. His view is that she’s distrust worthy, lazy and rude yet, I don’t see or get any of that. I see her as a kind, intelligent and thoughtful kid who loves her family and friends. She’s just a new teen going through shit IMO. Pleeeease help! What can I do to help this??