Hilary Duff Divorce -- Child Custody Fight On

EXCLUSIVE

Hilary Duff's estranged husband isn't giving up their son without a fight ... Mike Comrie just responded to her divorce filing, and is demanding joint custody. 

In the docs, the ex-hockey star says he wants to share custody of 3-year-old Luca. As we previously reported ... in her divorce petition, Hilary asked for primary physical custody of Luca -- and only wanted Mike to get visitation.

Sources connected with the couple say Hil is worried about Mike's parenting due to his partying ways.

Comrie acknowledges they have a prenup -- just as Hilary did -- to sort out their property and support issues, but clearly ... little Luca is going to be a point of contention.