Father and Son stories?

Yes but depends on what you consider strong, there's Ty father who I think he idolizes but he would learn things and secrets about him later that change his mind in some way, there's Taylor father who is also a Firefighter and *spoilers* he dies in the 9/11 incident and I think it affects Taylor and her family and there's also Bobby's father, I haven't watched season 1 and 3 so I can't tell you much but you should see the episode "Unfinished Business" this episode centers on Bobby and his father relationship and issues.

There's bosco and his dad in a few episodes in season 5.

Faith and her daughter in later seasons is similar to Mark and his daughter in the few seasons before his death.
In season 1 of Third Watch Davis was living with his mother. I wouldn't really compare it to the Mark Greene and his father story though.

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"Be the change you wish to see in the world" ~ Gandhi