Help them get a little closer
Go shopping together for a sling-type carrier, which puts a baby close to her dad (and doesn't have a lot of complicated buckles and straps). Then encourage him to wear your baby in it often. This physical closeness is a very natural way for them to bond, and (bonus) he'll have his hands free to help out with the dishes!
Baby wearing is especially helpful during the witching hour -- the end of the day, when kids of all ages are prone to fussiness and meltdowns. This is a time when a dad can really shine. He can wear his baby around the neighborhood for some bonding time and exercise, while you take a nap or do something just for yourself.
Have Dad start from the bottom up
Your child will need thousands of diaper changes during the first few years, so why not make these hours count? Even just changing a few diapers a day is a great opportunity for bonding.
Encourage your partner to view diaper changing as fun time with the baby rather than simply a messy chore. But take it from me: You'll have more success with this if you don't scold him for doing it "wrong." There may be a few messes at first, but in no time he'll get it right.