Sleeping on your belly protects your heart and makes you feel less physically vulnerable, which is why experts put this sleeping position down to anxiety and insecurity. It also shows that you might have trouble sharing emotions, i.e. you're a closed book. This might be occurring for very good reason, especially if one partner is abusive or overly dominant in the relationship.
If you sleep on your stomach with your partner, it might be time to have an honest chat about why you feel so vulnerable and closed up around them. If you notice that your partner is the one sleeping on their stomach, try to hold them close during the night if they'll let you. Show them that you're there for them both physically and emotionally. Talk to them about what's holding them back and help them release some feelings.