Mary's father has never spent money in spite of being a mill

不是,in spite of 后面不只是可以加名词的.还可以加其他的.
Mary's father has never spent money in spite of that he is a millionaire.这里也是可以的.
再问： 如果不加that呢？还有，你说的这句句子我怎么没见过？这里的“in spite of that ”算什么？
再答： 不加that 是不行的。好吧，这样的句子你没见过我就不说什么了。in spite of 相当于连词了。