Is "Both of our child" valid?

Question

Child: I am Papa's child. I am Mama's child.
Mama: Oh, so you are both of our child?

Is Mama's reply correct?

I want to use "both of" in my reply. How should I form the sentence if the above sentence is wrong?

Answer 1

Child: I am Papa's child. I am Mama's child.

Mama: Oh, so you are both of our child?

Both X or both of X means two/a pair of X together. There is one child, so both can't be used this way to refer to the child (keep reading, though).

There are two parents, which form a pair, so you want to use both referring to them. This is likely what you are looking for:

Mama: Oh, so you are the child of both of us?

or

Mama: Oh, so you are the child of us both?

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Now, if the parents were responding to the child with a joke or sarcastic retort, then Mama might say:

Mama: Oh, so you are both of our children?

The plural of child is children and since both refers to two things what follows has to be a plural.

Answer 2

Oh, so you are both of our child?

is incorrect. You can't say you are both, because both refers to you, and there is only one of you. I would say:

Mama: Oh, so you are our child?

This automatically implies both parents, when Mama says "our".

To write this concept using "both":

Mama: Oh, so you are a/the child of both of us?