Pulling it - manual removal - would be my first choice. If that proves to be too much of a burden, you could try something like Ortho's Grass B Gon, which only targets monocots (grass-like plants) and should not harm any more desirable plantings.

Suggest to your husband that RoundUp (not Round off) should only be applied where there is no potential to drift or come into direct contact with any desired plantings. Not a good choice to use as an effort to control weeds in any planting bed.

You can take a large piece of cardboard and use it as a shield for plantings you don't want to get spray on.

strategically it may be better to start with the milder interventions and save the big guns when all else fails such as dealing with an infestation of a noxious weed or poison ivy. Better for garden, small things like children, puppies and kittens and really small things like worms and insects. I know, Round Up is supposed to be non toxic to the above, but why apply to ordinary grass when a wee bit of muscle will do? So yes to both of the above.

Is your mulch three inches thick? I love the product mentioned above. The Ortho grass killer. It takes all the fear out of removing unwanted grass in planting area. It will not work on nutgrass, as it is not grass.

I was worried about a lab puppy licking weed killer off of weeds that I sprayed so I tried EcoSmart weed and grass killer from big box store. It says that its safe for pets and kids. It actually works REALLY well on grass growing up in beds. You might want to give that a try.