Can I claim the dependent care credit, if the daycare was paid through the other parent's paycheck, even if I helped pay for Daycare?

My children's daycare is connected with their Dad's work, so he pays for the daycare directly out of his paycheck and he also receives a discount for the daycare. However, I give him money to cover most of the daycare expenses. The Daycare is under both of our names, but it comes directly out of his paycheck. If I am claiming the children this year can I claim the Daycare expenses?