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

                Is it haram for someones wife to read quran next to her husband?
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.