Preface: you really should talk to a real estate attorney, estate attorney, and a CPA knowledgeable in this BEFORE you make any agreements. It is always cheaper and easier to do things right the first time.
First re: Capital Gains. You may have capital gain depending on what your adjusted basis in the property is. If your parents are buying 50%, then your proceeds for tax purposes would be 50% of the FMV of the property at date of sale (any difference between 50% FMV and cash/benefits received would be a deemed gift as this is a related party transaction). You would offset the $120k with 50% of your basis ($107.5k) resulting in a net gain of $12.5k. That is assuming 1)that your basis is your purchase price listed in your post and 2). you have not taken depreciation.
Their investment would be 50% of the market value, though as I mentioned you can gift them the difference between the mortgage balance and 50% FMV (though you still count the full 50% FMV as proceeds).
Your parents could gift easily without any tax with either proper reporting or proper planning. Assuming you are married and your parents are as well, $56k could be gifted in 2017 without tax or reporting and another $56k in 2018. Since we are so close to the end of the year this could work well. If they want to gift the full $105k in 2017, they just need to file a Form 706 gift tax return to report it. Unless they have already used up their estate exemption there should not be any tax.
EDIT: I should note that if you go the gift route your parents would not have an equity interest in the property, which seems to be the intention of this hypothetical. If they "gift" you money to pay off the mortgage and then you "gift" them equity in the property that could raise some red flags, though I must admit that this particular area is outside of my expertise.