The second one sounds like both people are your mother and your father, so each of them has two roles. The first one sounds more natural and common. “These” usually needs a plural and you are mentioning two single nouns.

The first one is correct however you could also say say instead, These are my parents

Unlike Chinese, in English it's more natural to refer to one's 'mother and father' rather than 'father and mother', just so you are aware. 🙂

I think both are grammatically correct.

This is my father and my mother. These are my parents.