"the incompatibility between" is correct and usable in written English.
You can use it when you are referring to two things that are not compatible or that do not go well together. For example, "The incompatibility between the two cultures led to serious tensions in the region."
But it's also etched in the incompatibility between Sam's career and his rowdy personal life.
This sprawling novel uses tennis as the focus of one of three interweaving plots, each designed to explore the incompatibility between human autonomy and playfulness.
Moreover, neither secular biologists nor religious fundamentalists will see it as a sign of cognitive health that so many Americans fail to perceive (as they do) the incompatibility between the two accounts of human origins.
As soon as the style of the play's nominal star, Kathie Lee Gifford, makes it clear that genuine comic attitude will turn into performing attitude while she's around, one begins to detect the incompatibility between collaborative lightness and star tripping.
The lawyers said the incompatibility between provisions for exemplary damages and the Human Rights Act is "so striking that no minister of the crown" would be able to get it on to the statute books.
A popular target is the incompatibility between the group's claim to adhere to strict teachings of the time of the Prophet Muhammad and its savvy use of modern technology such as Twitter.
John Paul showed himself generally unwilling to accept the incompatibility between Catholic social proscriptions and the drive to improve women's lives, particularly in the developing world, and in 1994 he declared that the church had no authority to ordain women into the priesthood, shutting down all discussion of this issue.
Notable examples are the incompatibility between classical mathematics and intuitionist mathematics, and the incompatibility between ZF-like universes of sets respectively with, and without, the Axiom of Choice.
Chander ([1993]) verified the incompatibility between core convergence property and local strategy proofness.
On the surface, the incompatibility between general relativity and quantum theory might seem rather trivial.
In fact, the incompatibility between the characteristics of the modeled variability just described and the observed variability precludes this.
