My brother and his spouse both passed this year. How do I file taxes for both?

I'm sorry for your loss.  If you are responsible for filing their income tax returns, you can file the way they ordinarily would have. In the past, if they filed joint returns, you can file a joint return.

When someone dies, the person responsible for the estate is the one responsible for filing the final tax return, if one is due. That person can be the administrator or the executor of the estate, or if there isn't one, it can simply be a survivor (you). 

You'd file the return(s) the same way as if they were alive, but indicate that they are deceased and the dates of death. If there is a refund due you would file a  Form 1310, Statement of Person Claiming Refund Due a Deceased Taxpayer with the return.

TurboTax has a complete discussion of how to handle a deceased person’s return here.

Here is a link to information from the IRS concerning filing a final tax return for a deceased person.

If you file separate returns for each of them, your brother would be filing as Married, Filing Separately, and his spouse would file as Single, because she would be considered Single at the end of the year. It's unlikely that this filing status would be beneficial.

[Edit 02/14/18 8:26 AM]