@easygoing,
What state are you in?
Likely, the $360 is calculated by taking into consideration the $160 you pay for health insurance. I would argue that the tax exemption should be divided 70/30, based upon percentage of income (assuming a 40 hour week for both parents).
If dad didn't have a shitty job, he'd be paying more child support.
In my state (Arizona), the cost of private school tuition is sometimes included in the child support calculation (education expenses). If not, it is often divided based on the 70/30 percentage. If you want the child to attend private school, and the education expense is not included in the child support calculation, then you should pay 30%, not 50%, based on the 70/30 split.
So, no, you paying half does not sound fair.
What's wrong with public school?