When your family includes your parents

there is no longer the need to make a distinction. A coworker named that group of people: "Farents".

So, if you feel the need to specifically call out that your family includes your mom and dad, you need only use this one word.

Related terms:
Fin-laws (your spouse's family)
Fids (your family when your kids are included)
Fiblings (your family when brothers and sisters are included)