Yes, your basic thinking is correct however it is not the beginning balance of each month, rather the ending balance or the AVERAGE balance for each month. (which would only matter if the loan was paid off or initiated that year)
So for each month, add ending balance, divide by the number of months you had that loan. For the partial month, you could add the balances each day and divide by the number of days. Add the balance for the first loan with that of the second.
Be aware that the TurboTax application cannot do the mortgage balancing for you.
You will need to calculate the allowed interest on your own, enter the 1098 Forms and at the end of the interview select to edit the amount of interest allowed.
Also, be aware that averaging may be counter-productive if one loan has an interest rate significantly higher than the other loan.
As long as the average interest allowed by averaging is more than either of the two loans individually, the average would be a better choice.
Pub 936
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