Although Catherine was pregnant many times, only one of her children, Princess Mary, survived. Henry was a doting father and didn't seem to blame Catherine for her failure to bear healthy sons. Henry is only known to have had two mistresses during his marriage to Catherine, which made him a reasonably faithful husband by the standards of the time. Catherine knew of his affairs but kept silent.
Caterina was related to both of John of Gaunt's wives, Constance and Blanche, and thus her line goes back to Edward I.