Hi - my name is XXXXX XXXXX I'm a Family Law litigation attorney. Thanks for your question.
Support obligations are determined by calculating the disparity in parties' incomes. If a child spends 40% or more overnights per year with a noncustodial parent, a rebuttable presumption exists that the noncustodial parent is entitled to a reduction in their child support obligation.
If the parties have equally shared custody there may not be a support order if their incomes are substantially the same. If one parent makes more money than the other, there will generally be an order for child support even if the parties equally share custody.
In your case, if you alternate 3 nights and 4 nights, then you should end up with practically the same amount of time with the children.
Thus, the only issue would be your incomes. Even if your time with the children is the same, if one of you makes more money than the other, the court can order one parent to pay support to help cover the costs associated with custody when it is being exercised.
Also, even if the father is not employed at the moment, the judge can base support on what the father should/could be earning if employed; the judge can also order the father to find a job asap.
Thus, it is possible that the court could order child support even if visitation time is equal. However, the judge could find that there's no need for support because of the similar income and time with the children.