In Chapter 26:

At the further end of the village, and tolerably disengaged from the rest of it, stood the parsonage, a new–built substantial stone house, with its semicircular sweep and green gates; and, as they drove up to the door, Henry, with the friends of his solitude, a large Newfoundland puppy and two or three terriers, was ready to receive and make much of them.

So Henry's estate at Woodston was the parsonage, and Henry was (presumably) rector of Woodston and held the Woodston living (from the General).

What does that mean should Henry die shortly after he marries Catherine? If Woodston is the parsonage, it would pass (with all Henry's improvements) to the new parson; so Catherine would have to move. Assuming no additional income from an ambivalent General, she would presumably have to live on what Henry has willed her, and consequential money from his mother's marriage settlement comes to Henry only on the General's death.

Of a very considerable fortune, [Henry] was, by marriage settlements, eventually secure; his present income was an income of independence and comfort.... (Ch. 31)