My friends and I are trying to come up with a list of dramas in which both parents of the leads are alive. So far we have Marriage Not Dating, Smile, You, Heard it Through the Grapevine and I Summon You, Gold. If you know of any others please let me know. 

My father is strange
Wang's Family
Smile, You
All About My Mom
Glorious Day
My Daughter Geum Sa Wol
Smile, Dong Hae

As you can see, they are all family drama lmao.
Boys over flowers. (korean version) .  His father is dead,  but no ^_^ how could you forget that.. 
Goong
The moon that embraces the sun (at the beginning)
Tomorrow's Cantabile
Thank you all so much! :D