It very well could be taxable.
If the parents chose not to "accrue" the interest - pay tax on it every year - but instead chose to defer the tax until redemption, then that interest is considered "income in respect of a decedent, (IRD), and someone has to pay the tax on the bonds. It could be the final income tax return of the decedent or it could be taxed as part of the estate. Otherwise, you probably will pay. There's no "step up" on the unpaid interest allowing it to escape taxation, unlike step up on an appreciated security where all the "built in" gain at time of death escapes taxation.
You might want to read this:
https://www.irs.gov/publications/p550#en_US_2017_publink10009922
Tom Young
