No, it is not normal for your boyfriend to be staying overnight with his wife and child if he is in a romantic relationship with you. This situation suggests that he is still involved in a marriage while also being in a relationship with you, which is commonly referred to as "cheating" or being involved in an "affair."
In a healthy and committed relationship, partners are expected to be exclusive and devoted to each other. Engaging in intimate or romantic activities with someone other than your partner violates the trust and commitment that should be present in a monogamous relationship.
If you are aware of this situation and feel uncomfortable or hurt by it, it's essential to communicate your feelings with your boyfriend openly and honestly. Addressing the issue will help you both understand where the relationship stands and whether it aligns with your expectations and values.
If he is still involved with his wife, it might be necessary to reevaluate the relationship and decide what is best for you moving forward. Trust and mutual respect are fundamental components of any successful relationship, so it's essential to address any concerns or discrepancies as early as possible to avoid further emotional distress.