The basis attributed to IRA assets that you inherited remains the same. Since you are a spouse beneficiary and you elect to treat the assets as your own by transferring them to your own IRA, the basis is now treated as if you made the non-deductible contribution. Going forward, you should file Form 8606 to determine the taxable portion of distributions you receive from any of your Traditional IRAs. If you also made non-deductible contributions to your IRA, the basis from the inherited assets should be combined with your basis.
This question was answered by Denise Appleby