Q. When believers die, do they have bodies in Heaven or are they invisible spirits?
A. According to my understanding, beings in the spiritual realm are visible to one another but not to beings in the physical realm. For example, in the story of the rich man and Lazarus the spirit of the rich man could see the spirits of Abraham and Lazarus (Luke 16:23) all of whom had died. Also, it appears that angels can see each other, but we can’t see them unless they either take on physical form, or God “opens” our eyes to allow it. Hebrews 13:2 says that some of us may have entertained angels without knowing they were angels. And God “opened” the eyes of Elisha’s servant in 2 Kings 6:17 allowing him to see the angelic warriors on the hills around him.
When believers die and go to be with the Lord, they are not given new physical bodies, but exist as spiritual beings. From the above I think it’s safe to say they are visible to other believers there. They will receive new physical bodies at the resurrection that accompanies the rapture (1 Thes. 4:16-17) after which they will be visible to anyone in the physical realm as well.