Nobody has the Force, it's just a shorthand way of saying that somebody is Force sensitive and can use the Force. The Force in the Star Wars universe is closer to what we would think of as an energy or a field for those of a physics disposition.
Force sensitivity comes in varying degrees but is an incredibly rare trait in any species outside of a select few. The Skywalker kids were much more attuned to the Force as their father was literally born as an expression of the Will of the Force rather than having a distinct father. Palpatine's old master, Darth Plagueis completed the work of his master Darth Tenebrous who was a Bith but also a genius engineer who had been trialing genetic variations in an attempt to create such an entity but was ultimately slain by his apprentice before hand.
Whether the combination of Plagueis and Palpatine managed to create Anakin Skywalker themselves is up in the air but it's heavily hinted that Anakin was NOT created by the Dark Lords but instead was the Force's reaction to their attempts.
Han wasn't Force sensitive and his kids, now considered non-canon since the Disney buyout, got their Force sensitivity from the bloodline of Skywalker through Leia.
Force sensitivity is something that is a split between various characters throughout the Star Wars Universe who believe very different things about it. Midichlorian count was a Jedi belief rather than an objective fact. Palpatine actually laughed at them for using this as a measurement system of Force sensitivity. Many believed that it was a living thing which had a "will" and even "desires" such as Qui Gonn Jinn and most of the Jedi, preaching that instinct should be relied on above all others. Others such as Palpatine and Yoda believed it to be nothing but an energy source with no real morality of "light" or "dark" inherent to it in a system known as the Unifying Force which was concerned with prophecy and destiny.
In fact the philosophical war between the ideas of the Living Force and the Unifying Force is the more interesting Star Wars idea, and it doesn't split along Jedi/Sith lines.
It's worth remember that the galaxy far far away has hundreds of billions of people living in it across thousands of worlds. Most of them would live their lives and never meet a single person who even met anybody who was Force sensitive. The Jedi and the Sith are for all intents and purposes a bit of a myth. Much of the armies in the Rebel Alliance and the Republic below them considered them all as bad as each other like Gods fighting amongst themselves on Mount Olympus with the collateral damage of millions of normal people dying.
To Han in A New Hope, the Force was a tale of myth and legend because as a normal traveler he had absolutely no reason to believe it existed any more than dragons do
