I inherited a non-qualified annuity from my parents.
Am I taxed on the interest earned on the annuity or on the full amount of the annuity?

The difference between what you receive and what your parents invested is taxable income.
Thus
*the money you receive is fully taxable until you have withdrawn all of the earnings. After that, all withdrawals would be tax-free, or
* for each payment received a part is taxable and a part (return of capital) is tax free.