You have it right. Jesus was conceived into a human being, but He still retained his divine nature. Thus making Him God and Man. Immaculate doesn't mean someone is conceived into a human being--The word Incarnation means that--The word immaculate means "sinless". Jesus and Mary both fall into that category. The difference being that Mary is the most perfect human creation of God whereas Jesus was not created, but always was God. Mary was cleansed from Original Sin and made a pure and unstained soul that could bear the Son of God without any impurity of sin.
In any case, the Dogma of Immaculate Conception refers to Mary as can be seen in the solemn definition of the dogma promulgated by Pope Pius IX which reads:
Apostolic Constitution of Pope Pius IX solemnly defining the dogma of the Immaulate Conception, 8 December 1854.
...Accordingly, by the inspiration of the Holy Spirit, for the honor of the Holy and undivided Trinity, for the glory and adornment of the Virgin Mother of God, for the exaltation of the Catholic Faith, and for the furtherance of the Catholic religion, by the authority of Jesus Christ our Lord, of the Blessed Apostles Peter and Paul, and by our own: "We declare, pronounce, and define that the doctrine which holds that the most Blessed Virgin Mary, in the first instance of her conception, by a singular grace and privilege granted by Almighty God, in view of the merits of Jesus Christ, the Savior of the human race, was preserved free from all stain of original sin, is a doctrine revealed by God and therefore to be believed firmly and constantly by all the faithful."
Thanks for the clarification!