"are both like" is grammatically correct and can be used in written English.
Example: Both Sarah and Tom are both like cats, always napping in the sun.
But, by One-over-Many, A and B are both like by virtue of partaking of a form of likeness (say, L1).
Debbie and I are both like that.
Our families are both like modern American families.
They are both, like the towering statue of Salif Keita nearby, high-maintenance spiritual celebrities.
She is creating a dialogue that shows us how we are both like, and unlike, the Romans".
My mom and dad are both like 43 years old, so our relationships are more like sister and brother than mother and father.
Again, you'll be more successful if you are both liked and smart.
They were both like, "Shawna, please".
And she and I kind of both made eye contact at the same time, and we're both like, "Surprise!" at the same time -- like, simultaneously.
He is both liked and respected on the Street.
"He is a very professional athlete who is both liked and respected by the rest of the team.
