First you need to decide if you have a rental situation or only a room mate situation.
If this is merely a cost sharing arrangement where the amount paid is below fair market rental, there would be no reportable income to you. If the “rent” amount is fair market value, or more, there is still some question as to whether you even have to report it, as it almost always comes out zero. Most people take the attitude that it is not income; it's just room mates sharing expenses and ignore it. Family, as opposed to unrelated roommates, makes that position stronger.
Here’s what you may be required to do:
Report the income (enter at Rents & Royalties/Income & expenses from Rental Properties); and then deduct the expenses on schedule E. If the room mate has full run of the house, and there's just the 2 of you, then half your expenses are deductible (mortgage interest, property taxes, insurance, utilities, repairs, and depreciation [if needed}). Your net income will usually be less than zero.
What you are NOT allowed to do, because it is your own home (you have "personal use") is claim a loss from this activity, to offset other income. Because of the "personal use rule", your deductions are limited to your income. Net effect ZERO.
TurboTax (TT) does not handle this properly. TT will not limit your deductions to your income. You have to do that manually. TT wants you to enter this as a “not for profit rental”, which does not use Schedule E and puts your expenses on Schedule A (itemized deduction). I'm of the opinion that's not the proper way.
As to who reports it, you follow the money. Since all expense are split 50-50 as well as the income from the rental, you each report half. The comment about personal use applies to you as well, since you are allowing a family member to live in "your half".
