Honestly, she's so tiny that she's probably still at the stage when she doesn't really consider you as a separate person from her.
It's so hard when babies are like this, I remember it so well. My youngest would literally only sleep with me, if she was on top of me. Her dad could rock her to sleep and then put her down. And she'd stay asleep. I would rock her to sleep and within seconds of putting her down she'd be screaming as if I was torturing her. It was awful.
But, your baby has spent her entire existence with you. Your smell, your heartbeat, your voice etc are all just an extension of her, as far as she's concerned. So when she's with you, and she cries, it's not a reflection of her feelings for you. It's just that she's not acknowledging you as a separate person at all. You're a part of her as far as she's concerned.
She will recognise your partners voice etc when he has her. So she'll calm down for him - not because she likes him better. But because she sees him as a familiar person. He's safe.
You, however, are her world. A part of her. It's so SO hard when you are living it. But be kind to yourself. She doesn't like you, she loves you. You are everything to her.
This time will pass. She will get bigger and learn to recognise you as 'her mum'. Sometimes she will seem to prefer you, sometimes she will seem to prefer your partner. Sometimes she will declare that she hates you both (I have a teenager - fun times!). For now, just take each day as it comes. If she settles for your partner and is content, then take yourself of for a bit and do something for you, have a bath or a rest.
Keep telling yourself that she LOVES you - she absolutely does, I guarantee it.