This is the proper concept of Incarnation.
Please note the importance of the word Person. The words person and nature are precisely used in Catholicism.
There are three Persons, real Persons, in the divine nature of the Most Holy Trinity. Each Person, Father, Son, Holy Spirit has a divine nature.
A person has a specific nature. A human person is not a dog or a bear because a person has a specific human nature and not a dog nature and not a bear nature. Each Person in the Most Holy Trinity is divine because the specific nature of the Most Holy Trinity is divine. A human person cannot change his nature when it rains. God also has an unchangeable nature.
I realize and accept the fact that a person with a human nature will have difficulty with the concept of three separate Persons having the same single nature which is divine, not human, not dog, etc.,
Jesus Christ is a divine Person. Because His divine nature is greater than a human nature, He can do more things than a human person can. Because Jesus Christ is a divine Person, He can assume human nature which means adding an additional nature to His divine Person. Please note that He is not changing His fundamental nature, He is adding a nature to His Person. His Person assumes a second nature which happens to be a human nature. His Person has a divine nature; therefore, He is capable of assuming a secondary nature per se.
Please note that Jesus Christ assumes human nature as a pure human nature without any kind of sin. Jesus Christ, having a divine nature, does not have to sin in order to assume human nature.
Because Jesus Christ is divine, He does not have to change His nature to human. All He has to do is to take upon Himself (assume) the separate human nature. Assuming a human nature does not require that the Person Jesus Christ change His divine nature to a lower level.
One way to remember the above are these two sentence. God is three Persons in one Nature. Jesus Christ is one Person with two Natures.