Funfact: Anna Menon's husband, Anil Menon, was recently selected in the NASA space corps. It would be fun to see if Anna Menon ends up flying before Anil Menon.
Would they be the first couple where both partners went to space?
Definitely not. For a recent example, both Bob Behnken and Doug Hurley of the first manned SpaceX Dragon crew have astronaut wives, (Megan McArthur and Karen Nyburg, respectively).
Jan Davis and Mark Lee, a married couple, both went up in 1992 on the same flight, STS-47. (I think they actually were selected prior to being married, and got married in secret during training, but I forget the exact timeline)
It's basically assured that Anna will fly before Anil. Anil's got to do 2 years of astronaut candidate training, then become an astronaut and wait for a flight slot.
Remember the epic "Navy Seal + Harvard Doctor + Astronaut" guy still hasn't flown.
Would they be the first couple where both partners went to space?