If one member of a couple is retired and the other is still working, can both contribute to a Roth IRA and an HSA?

The requirements to contribute to an HSA is that the taxpayer (even just one of you) is covered by an HDHP policy and is NOT covered by any conflicting insurance. For example, if one spouse has a Self-only HDHP policy and the other spouse is on Medicare, this is not a problem so long as only the spouse not on Medicare makes the contributions to the HSA.

The requirements for contributing to a Roth IRA are unrelated to those for an HSA; please see this IRS webpage for Roth IRAs.

Although I do not know your particulars, there is no intrinsic reason why you can't contribute to a Roth IRA and an HSA in the same year, bearing in mind what I said in the first paragraph about HSA contributions.