Possibly. But there has to be two separate households, because only one person can pay "more than half" the expenses of any particular household.
Suppose you and your child live in a 4 bedroom house and rent the other two bedrooms to a friend and their child. You aren't related, you keep separate pantries, and pretty much have separate friends and social life. You are pretty clearly two households and different people might possibly be heads of each separate household.
But suppose the renter is your sister and the kids are cousins, and they play together, go to school together, you share household expenses, food, etc. and have a common social life. You are pretty clearly one household, so only one person can be head of that household, and that person has to both pay more than half the total common household expenses and provide care for a qualifying dependent.
You have to evaluate your own circumstances.