No, you cannot not file a 2016 tax return in his name. Legally, distributions to your husband were not permissible after the date of his death. Contact the payer to obtain corrected 2015 and 2016 Forms 1099-R to show the amounts distributed after the date of his death as being distributions made to you as beneficiary instead.
If you filed a joint tax return for 2015, the corrections to the 2015 Forms 1099-R probably will not result in a change to your 2015 tax return for which you would need to file an amendment, but you should check to be sure.
With the corrected 2016 Form 1099-R for 2016 distributions you'll file this on your own 2016 tax return.
