"This is mom and this is dad."
Translation:Це мама, а це тато.
When you are referring to your parents as to a group, use "і". Here you are introducing different persons, so you better use "а" (instead of "і") which can be translated 'whereas'.
"Це мама, і це тато" would put an excessive emphasis, like 'this man is really my dad, not somebody else'.
When introducing several people or showing several objects "this is A, this is B, and this is C", use "а": "Це А. це В, а це С"