there was no kiss or sex between the dad and the girlfriend(maybe later on :s), but their relation became closer.
the father and the Gf text and call each other, (i didn't understand much)
there was time when the GF blush when she was with the father, and the father saw his dead wife in her, further more most of the panel with the father and the GF show some twinkle background.
there was a chapter when the father take the gf home in his car after her work( she was nervous to be with him) when they arrive, the dad get off the car (it was raining) took her off the car and shared an umbrella but the bf saw the two of them enjoy their time (it was like they where together), sometime after that the bf try the look the phone of his gf secretly without success.
one day the two of them goes to her house the bf wanted to bang but she didn't want. meanwhile the he remember the scene between her and his father, got angry and left the house, the gf try to chase after him but it was raining.
at her job, she was dizzy (she catch a cold)and collapse the father was there, took her to the hospital and remember his wife.
later on the couple where at a restaurant with the girlfriend's friend, the gf phone rang(maybe it was the father) the girl leave the table and answer (the boy didn't see the number), the friend and the bf talk about the gf and how he should take care of her.