There was an action code named Operation Market Garden, which involved the First Allied Airborne Army, made up of US and UK units. My references confirm that US 82nd A/B was involved, but I can't identify the British elements right now.
Nijmegen, Grave and Arnhem were primary objectives.
Stanton states that the British Guards Armored Division was at Grave, Holland, which is just below (5 miles) Nijmegen, so there were ground forces from UK there, as well as airborne.
This operation pushed off 17 Sep 44, and proved to be a tremendous blunder in planning. Heavy losses were endured, and the operation was canceled 25 Sep 44.
Does your grandmother have any idea as to her husband's unit identification...old letters, newspapers etc ?