Death is a part of reality. When somebody close to us dies we are sad. There is a feeling of loss because someone who was a real part of our life is no longer going to be there in the same way.
This real process of grieving is the same for all of us. It is a part of being human.
Maybe having faith adds another dimension to this. The idea that some part of someone we care about continues to live on is certainly comforting. When I was religious, someone close to me died of terminal cancer. We said our goodbyes and as Christians we left with an understanding that we would see each other in heaven. And sure, this provided comfort. This didn't really stop the grieving process for people who were close to her.
Having this faith, or as you put it other dimension, doesn't take away from our shared human reality. Calling it sleep or talking about an eternal afterlife doesn't change the reality of death.