Orbitting light dissappears then becomes two objects

Me and my wife walk in the mornings before the sun comes up almost every day of the week.  It was a clear sky so we were admiring Jupiter in its bright glory in the western sky when I noticed an object, nearly as bright as Jupiter appear behind Jupiter and move quickly towards the north-east.   At the time I thought it to be the International Space Station as I’ve watched it travel overhead and the brightness and speed were very similar.
I continued to follow its progress across the sky until when it reached nearly overhead, it disappeared for a moment and then reappeared as two identical lights traveling along the exact same course at the same speed as before it disappeared.
The objects appeared to me to be in orbit and when the one object became two they were separated by about a ½ fists width at arm’s length.
When I got home from work later that day I checked one of the orbital spotting websites and did see that the IIS was traveling overhead near the time we viewed the event.
I've been an avid night sky watcher for over 35 years and in all those years I've never seen anything like this before; I have no clue what could have caused what I saw.
Witness indicates that the date of the sighting is approximate.  PD