What do you think about this proposition/investment?

i currently live in a rental property owned by my father.i pay half of the normal rent.he is actually breaking even and not making a profit cause he is out 600.00 a month.so today he told me a proposition he had for me.i would move back into my parents house and live in there basement(fully finished with a bedroom and a living room) and he would give me 100.00 a week and i wouldnt have to pay any rent.that will help me get my finances in order.then in 6-12 months he would put the down payment on a house for me (60,000..we live in long island ny) and put it in my name with him as the co signer.the house would be a high ranch so i would have one floor and rent out the other floor.so with the other persons rent and my rent it will pay off the mortgage payment for the month.then eventually he will take his name off the house and it will be mine.im almost 29 and i would never be able to afford a house here on my own because the cheapest houses here are a little under 300,000.00 .the only people that live in my parents house is them and i would have privacy.they dont bother me at all and i am very close to them.i guess the only issue is that even though i have privacy my parents (my mom especially) are olf fashion italians off the boat and wouldnt agree with my bf sleeping in the same bed as me(he is in the military and is stationed in a different state).i brought that up to my dad and he said well you lived with your x and you went on vacations with guys so its a little late(for the talk lol) i guess i just wanted to know your opinion on this.PLEASE MATURE ANSWERS ONLY!!!!