If my parents and I have a house as joint tenants, and my parents live there and pay me $500 per month (less than fair market value) on the house we hold as joint tenants, do I have to report the $500 per month as income?

you do not need to report $6K;$500*12 as your rental income; You co own and are sharing space and expenses. You are NOT charging RENT and you are NOT renting to them.
You are NOT renting out the home.
a family living together and sharing the costs. Even your mother gives and treats the whole of $6K;$500*12 as a gift, she does not need to file form 709 as $6K is LESS than $14K , annual exclusion from gift tax for 2015.However, if she decides give you,ONLY TO YOU and you do not share it with your parents, a gift money exceeding $14K, then, she NUST file form 709 with the IRS.


You and your parents may dedduct home related expenses , i.e., •Home Mortgage Interest payments
Real estate taxes;Mortgage points (each point is equal to one percentage of the loan amount);Mortgage Insurance Premium payments

on SCh A of 1040 aslongas you itemize dedcutions on your return;