This is a great question. As we read the story, Mr. and Mrs. White have a nice relationship. In particular, Mr. White is a kind man and does whatever his wife wants. We know this, because in a conversation, Herbert, their son, says that Mrs. White always bosses Mr. White around. Here is what Herbert says:
Wish that you were an emperor, father, to begin with. Then mother won’t order you around.’
As the story progresses, we can see this dynamic. Mrs. White does, indeed, run the show. So, when Herbert dies, Mrs. White makes Mr. White wish their son back. Mr. White is afraid and does not want to do so, but complies. Here is a conversation:
‘Wish!’ she cried in a strong voice.
‘It is foolish and wicked,’ he stammered, hesitating.
‘Wish!’ repeated his wife.
He raised his hand. ‘I wish my son alive again.’
In the end of the book, the relationship changes. When there is a knock at the door, and Mr. Herbert believes that it is their dead son, he is afraid, as Herbert has been dead for ten days. Against the wishes of his wife, he presumably wishes everything to do away.
So, in the end, Mr. White opposes his wife's desire.