Jack and Jill(ian) seem to be long acquainted with each other. Jillian indicates that she believed he had a crush on her. Jillian on her part seems at least fond of Jack and considers him to be a genius Foolamancer. However, she rejected his attempt to form a romantic relationship with her.
Even though she had no romantic interest in him, Jillian still considered Jack to be her best friend, and desired to repair their relationship. But it is likely that the damage caused to her mind by Charlie and Betsy removing the bits they didn't like made her forget the fact that their relationship had even been harmed in the first place.
When the two met in battle both seemed to be deeply affected; Seeing Jillian and hearing her speak his name appears to have largely cured Jack of the insanity caused by an improperly broken caster link. Jillian has offered to accept Jack to her side both times they have encountered each other within the comic. Both times however, Jack has declined the offer. Because of his painfully unrequited crush on her and his admiration of Parson's skill at "lateral thinking", he has thus far chosen to remain Gobwin Knob.