Money you pay your parents for the mortgage will be considered rental income
and they must pay tax on it.
Yes, the interest will be tax deductible for them.
When they sell the house to you, they will have to pay tax on the money from
the sale.
When you sell the house, the tax basis will be what they sold it to you for.
For instance, if they sell it to you for $100,000 and you sell it for $200,000,
you will be required to pay taxes on the difference.
Altogether, most people consider this a very bad idea.
Pat