If I ask for a child support increase, does the court take into consideration my new husband's income?

Depends on the State - in some State the thinking is that now you have more disposal income because someone else is paying a utiity, for example, instead of you.

It can, it will depend on where this is. ( where the court order is at)

Changes in support ( up or down) is based on incomes, often your income and the non custody parents income, but can be spouses also in some area. Also days child is with each in some states.

I'm in the state of LA.