It is permissible for each partner to read Qur’aan next to the other

Praise be to Allah.

It is permissible for a wife to read Qur’aan next to her husband and vice versa. What is haraam is to read Qur’aan when in a state of janaabah (impurity following sexual activity).  

See Question no. 10672. 

And Allaah knows best.