My daughter (who is now 15 years old) wouldn't go to anyone for the first two years of her life - except for me, of course. Any time her dad would take her to give me a break, she'd freak out and scream and cry for me. It was exhausting for me and hurtful for him, but we had no choice but to let it take its course. As I look over on the sofa right now, my husband and daughter are watching a movie, and my daughter has her legs stretched out comfortably on her dad's lap. Things have worked out well, I'd say.
Seriously, I just had to hold my daughter for her first two years, and then, when she was ready, she started reaching out for others. When she was a tiny baby, she'd go to him at times, but as she got older and developed a preference, it was always me. I was a stay at home mom and was with her all day - sometimes she'd be happy to see my husband when he got home, but usually she'd run to me to have me pick her up and she'd hide her head in my neck. It was heartbreaking - my husband really wanted to be close to her and also wanted to help me by giving me some time alone, but he was a trooper. The important thing is for your husband not to take it personally and to keep showing an interest - he can talk to her while you're holding her if that's where she's more comfortable - but he needs to stay present and connected so she can turn to him when she's ready. Encourage him to play peek-a-boo (or any funny game) with her when she's sitting in your lap - the key is for him to continue interacting with her even if she doesn't want to go to her. Light hearted, fun, and daily interaction will allow the two of them to relax and enjoy each other without putting pressure on her to have to leave your side (which is where she wants to be right now.)
I have another daughter who is a single mom. Her roommate is a very nice young man (they're just good friends) who loves babies. The problem was, when my daughter first moved in with this guy, my granddaughter (10 months old at the time) would freak out every time the guy walked into the room. They started doing just what I suggested - fun interaction while my granddaughter sat on my daughter's lap, and the roommate would just sing silly songs, play peek-a-boo, etc. for a few minutes, then let it rest. Long story short, after a month or so of this type of (daily) interaction, my granddaughter now runs to the roommate with arms flung wide open, and he picks her up and swirls her around like an airplane. When I went to visit my daughter the other day at her house, the roommate was sitting on the couch and my granddaughter was cuddled up in his lap, head against his chest - you get the picture. It just took patience, understanding and time.
Good luck with this...I know it's difficult, but it will pass if everyone can relax and let nature take it's course.
T.