There is so much in the show that suggests Ashi and Jack are meant to correspond to Yin and Yang, darkness and light, two halves of a whole responsible for balance and harmony.
If I’m not mistaken, Yin and Yang have a push and pull relationship, interdependent on each other. Jack’s influence allows Ashi to grow and flourish as a person, while Ashi’s presence causes Jack to experience a few light hearted moments in the midst of his depression and trauma.
What I love is that Ashi has been written and portrayed as someone who is both similar and opposite to Jack. Jack starts his journey garbed in white with a straight edged bladed sword. He is shining with compassion and determination to save his family and his people. Ashi starts her mission dressed in black and wields a Kusarigama, a weapon meant to take someone’s sword from them with a curved blade. She shows no compassion towards her sisters. Ashi was raised to serve Aku, Jack trained to destroy him. Jack traveled the world, Ashi was confined to a single location all her life. Jack was raised by loving parents, Ashi was abused by her mother with her father nowhere to be found.
(Trivially, Jack was an only child, Ashi has/had six sisters).
Jack has darkened throughout his journey, Ashi has lightened.
However, for all their differences, the two are startlingly alike. Both of them were trained to fulfill destinies tied intrinsically to Aku. Both are driven to help others and defeat any evil that plagues the world (this was true of Ashi even before she defected from Aku; in her rants towards Jack, she calls Jack ‘evil’ and Aku ‘kind’, indicating a large part of her desire to kill Jack, aside from being brainwashed into it, is because she wants to eradicate what she perceives to be the danger to the world.) Both show a natural kindness towards children. Both are skilled fighters in their own right. Both suffer hallucinations and have undergone trauma.
(On another somewhat trivial note, both as children were enchanted by insects; Jack a cricket, Ashi a ladybug.)
tldr: Jack and Ashi oppose and complement each other in many ways, which is shown in both their designs and their personalities.