I'm glad that DH and I never treated the kids like Mine and Ours.
My DD1 (from my first marriage) was treated exactly like our DD2 by DH. If she did something well or got a good grade or whatever, he let her know. If she was scared or hurt, he was there for hugs and to bandage her knee. He wrestled and tickled her, just like he did with DD2. If she screwed up, DH let her know---and would punish her just as he did DD2.
If he brought home something from the store or work for DD2, and DD1 was home, he brought her something too. When he went on business trips, he'd bring DD1 home a gift (even if she was with her father or grandparents).
If I had to work, he'd have both the girls (DS wasn't around then), without complaint. I never had to ask "Do you mind watching DD1?" The conversation would go: "I'm scheduled for Saturday." "Ok, I think the kids and I will go to breakfast and then maybe go see a movie."
Did he favor our DD? I'm sure he did. She had him wrapped around his finger since she was born. He didn't go through the baby phase with DD2 (she was 3 when we started seeing each other), so he didn't get that bonding time. But he never--not once---treated her differently than DD2 (when she was with us).
But not once did DH ever treat DD1 as anything less than a treasured little girl. Guess she was lucky, from what I read today.