Possessive pronouns indicate many things. Paul calls the gospel of Jesus Christ "my gospel" in three different places: Romans 2:16; 16:25; 2 Timothy 2:8. We may ask someone if a certain church is "your church" or "his church." We are not referring to actual ownership--only connection. We would not even have a problem with a reference to a "sergeant and his men" coming over a hill to attack. We know that those men are connected with that sergeant. He is in charge of them. They are his men.
The reference you refer to is Revelation 12:7 - "And there was war in heaven: Michael and his angels fought against the dragon; and the dragon fought and his angels." Michael is the archangel of God. That is, he is the general or the captain of the host. In this verse, he is the general in charge of military operations. The angels under him are "his angels."
As further evidence, we see instances in the Bible that are similar. When David was king of Judah, Joab was the captain of his army. In 2 Samuel 2:32, the Bible refers to the maneuvers of "Joab and his men." But, you could say, they were not Joab's men--they were David's men. Well, not according to the Bible. The Bible says they were Joab's men. In like manner, the angels of Revelation 12:7 were Michael's angels.
Be sure and click the link for the answer to the remainder of your question titled "Jesus and Michael the Archangel".