Not in the DNA sense. Here's why: Jesus was conceived prior to being implanted into Mary's womb, thus his DNA was not Mary or Joseph derived. All the children with DNA from Mary and Joseph (remember that feminine looking one in da Vinci's Last Supper; the brother of Jesus in the sense that they both have the same Mother who gave them life support in her womb) are brothers and sisters but not in the DNA sense. By the same token, I'm a brother of Jesus by the coming of the Holy Spirit but not by DNA.

A perhaps more intriguing notion is 'how much of Jesus did Mary retain in her body following His birth?' It is a known fact that a few cells of each child gestated in a woman's body are retained in her body for the rest of her life. [And folks don't want to acknowledge some holiness for Mary!]

[And folks don't want to acknowledge some holiness for Mary!]

She got 'holy' the same way the rest of us do:

By believing!

(And she's awaiting Christ's return the same way other dead believers are.)

1 Thessalonians 4:13-17

13. Brothers, we do not want you to be ignorant about those who fall asleep, or to grieve like the rest of men, who have no hope.
14. We believe that Jesus died and rose again and so we believe that God will bring with Jesus those who have fallen asleep in him.
15. According to the Lord's own word, we tell you that we who are still alive, who are left till the coming of the Lord, will certainly not precede those who have fallen asleep.
16. For the Lord himself will come down from heaven, with a loud command, with the voice of the archangel and with the trumpet call of God, and the dead in Christ will rise first.
17. After that, we who are still alive and are left will be caught up together with them in the clouds to meet the Lord in the air. And so we will be with the Lord forever. 18. Therefore encourage each other with these words.

"Jesus was conceived prior to being implanted into Mary's womb, thus his DNA was not Mary or Joseph derived."

I disagree. Mary was not the “surrogate” mother of Jesus. She was really and truly His mother.

First, I found this link, which explains the technical/biological side. The best tech explanation I’ve seen.
Q & A: Did Jesus have Mary's DNA? http://www.bibleanswerstand.org/QA_DNA.htm

CHURCH FATHERS A Sectional Confession of the Faith (St_ Gregory Thaumaturgus)
http://www.newadvent.org/Fathers/0605.htm
“Further, we acknowledge that the Son of God was made a Son of man, having taken to Himself the flesh from the Virgin Mary, not in name, but in reality…”

The Summa Theologica of St. Thomas Aquinas
http://www.newadvent.org/summa/403504.htm
“…she [Mary] begot of her flesh the Word of God made flesh…”

“Therefore He who is "above all things, God blessed for ever," is truly born of the Blessed Virgin as of His Mother.”

“…she is the mother, according to His human nature, of the Person who has both the divine and the human nature.”

CHURCH FATHERS On the Flesh of Christ (Tertullian)
http://www.newadvent.org/Fathers/0315.htm
“If it was not as her son, but only as a stranger that Mary carried Jesus in her womb, how is it she says, "Blessed is the fruit of thy womb?”

Father William Saunders
https://www.ewtn.com/faith/teachings/maryc1.htm
“Mary conceived by the power of the Holy Spirit. (Lk 1:26-38 and Mt 1:18-25) Through her, Jesus Christ--second person of the Holy Trinity--entered this world, taking on human flesh and a human soul. Jesus is true God and true man. In His person are united both a divine nature and a human nature.

the One whom she conceived as man by the Holy Spirit, who truly became her Son according to the flesh, was none other than the Father's eternal Son, the second person of the Holy Trinity. (CATECHISM OF THE CATHOLIC CHURCH, No. 495). Council of Ephesus (431)

Flesh of Her Flesh Mary Full of Grace
http://www.boston-catholic-journal.com/flesh_of_her_flesh_mary_full_of_grace.htm
“Grace is a participation in the life of God" (Catechism of the Catholic Church, §1997) – and Mary, the Angel Gabriel declares – is filled with it! Filled with the life of God, participating in the life of God as no other human being in history. She is full of grace, participates consummately in the life of God – even before she bore His Son.
Why?
Because she was to bear His Son. It was from Mary that Jesus took His Sacred Humanity. It was from Mary that He took His flesh, becoming like unto us in every way but sin.
How much closer can a human being be to God ... than to have given Him His very flesh ... enabling, yes, enabling God to become Man!
Jesus flesh was not different from Mary's – it was Mary's! ... just as his Divinity was not different from God's, but was, is, God's.