The ending of Street Fighter Alpha reveals how the two met.
Eliza is seen in Ken's ending of the Street Fighter II games. Following Ken's defeat of M. Bison, Eliza convinces him to spare the dictator's life, and Ken and Eliza get married.
In Street Fighter IV, Eliza is pregnant with their child, a story development from the Udon Street Fighter comics which inspired certain story elements of Street Fighter IV.
In Street Fighter III Eliza and Ken have a child together.