How should we think about Jesus' mother being Jewish and his father being the Holy Spirit?

Here's what I understand the Catholic answer to this question to be:

1. Jesus' Divine Nature comes to Him through the Father.
2. Jesus' Human Nature comes to Him through His Blessed Mother.

Jesus is one Divine Person with two natures.

However, Jesus' Human Body comes to Him through His Blessed Mother and no one else.

The Substance which materialized at the moment of the Incarnation was taken from Mary in the same way as the substance which made Eve was taken from Adam.

Regardless of who you are, it's up to God to animate your body with an immortal soul. It's not up to your parents. I'm more or less making this up, but it may even be part of God's covenant with Adam to subdue the Earth and fill it. The married couple supplies the baby and God will give him or her the immortal soul.

Calling the Incarnation "a miracle" is actually kind of lame. It is "THE MIRACLE", the one that, if you're paying attention, you should bend your knee and thank God for whenever it is mentioned!

Yes, it is a sin for a Catholic to deny that Jesus was born of a Virgin or to assert any other blasphemy against Our Lady's purity.

If God was capable of creating human beings to begin with, without benefit of pre-existing males or females, then it's no great leap to suppose he could create a human being with the "assistance" of a human female.

Presumably when he created Adam he created an entire body. To effect a virgin birth he would only have to create one cell, i.e. a sperm cell. Or less: he could have caused an egg in Mary to split in a process akin to parthenogenesis. He would have had to create a Y chromosome, and he may have decided to create other genetic material.

Of course, whether you believe in a God capable of such creation is a pretty fundamental question.

BTW, anti-Christians often say that people in Bible times believed in miracles because they didn't understand science and so didn't know that these events were impossible. This is ridiculous. The authors of the Bible were well aware that the virgin birth (and other such miracles) was impossible by every known law of science. That's why they described it as a great miracle, rather than a curious side note. If people back then didn't know that it was impossible for water to turn into wine, they wouldn't have said that Jesus performed a miracle, they would have said, "How convenient! The water turned into wine just when we needed it."

Update

Reply to Mr Gravell: Do I really need to give examples of people saying that the folks in Bible times only believed in miracles because they were ignorant of science? Okay, in a quick Internet search I don't find those exact words, but here are some examples of essentially that idea:

In those parts of the world where learning and science have prevailed, miracles have ceased; but in those parts of it as are barbarous and ignorant, miracles are still in vogue. -- Ethan Allen (quoted on Wikipedia "Miracle" page)

The people who tell these stories about miracles would make good storywriters. They would not make good science fiction writers. They possess little knowledge of science. -- http://www.jovialatheist.com/miracles.html (In context, he's talking about the writers of the Bible as well as people of later times who believe them.)

We may, in fact, say that a miracle is an event of which the causes cannot be explained by the natural reason through a reference to ascertained workings of nature; but since miracles were wrought according to the understanding of the masses, who are wholly ignorant of the workings of nature, it is certain that the ancients took for a miracle whatever they could not explain by the method adopted by the unlearned in such cases. -- Spinoza. http://www.sacred-texts.com/phi/spinoza/treat/tpt10.htm

Skepticism wasn't what it is today. Someone who tells you today that a demon jumped out of a tree, or a giant sea monster devoured a ship is likely to be ridiculed or sent to the Daily Sun. However, such tales were quite common and widely accepted with little question in Christ's day. -- http://www.infidels.org/library/modern/kyle_gerkin/objections_sustained/obj2.html

But a miracle means a violation of a natural law, and there can be no proof imagined that could be sufficient to show the violation of a natural law; even though proof seemed to show violation, it would only show that we were not acquainted with all natural laws. ... Primitive and even civilized people have grown so accustomed to believing in miracles that they often attribute the simplest manifestations of nature to agencies of which they know nothing. -- Clarence Darrow. http://www.infidels.org/library/historical/clarence_darrow/why_i_am_an_agnostic.html

In ancient times it was natural to ascribe the violent acts of nature to a pantheon of mischievous or malevolent deities. Calamities were often taken as a sign that we had somehow offended the gods… Ignorance of nature’s ways led people in ancient times to invent gods to lord it over every aspect of human life.” – Stephen Hawking and Leonard Mlodinow, The Grand Design, Bantam Books, p25

Etc etc.

The Bible makes it very, very clear that the virgin birth is true. The emphasis below is mine:

Matthew 1:20-23 ESV

"Joseph, son of David, do not fear to take Mary as your wife, for that which is conceived in her is from the Holy Spirit. ²¹She will bear a son, and you shall call his name Jesus, for he will save his people from their sins."²²All this took place to fulfill what the Lord had spoken by the prophet: ²³"Behold, the virgin shall conceive and bear a son, and they shall call his name Immanuel"

Luke 1:30-31, 34-35 ESV

And the angel said to her, "Do not be afraid, Mary, for you have found favor with God ³¹And behold, you will conceive in your womb and bear a son, and you shall call his name Jesus..." ³⁴And Mary said to the angel, "How will this be, since I am a virgin?" ³⁵And the angel answered her, "The Holy Spirit will come upon you, and the power of the Most High will overshadow you,; therefore the child to be born will be called holy - the Son of God."

"therefore the child will be called holy" - this statement explains the importance of the virgin birth. If Jesus had been born of man, he would be a sinner, for "in Adam all die" (1 Corinthians 15:22). However, since Jesus was conceived by the Holy Spirit, he is "holy."

Also, the angel's reassurance to Joseph that the child is from the Holy Spirit rules out any possible third party - unless you question the angel's knowledge.

tl;dr: you either have to twist the Scriptures like crazy or just outright disbelieve them to refuse the Virgin Birth.

EDIT:

Regarding the miraculous nature of the virgin birth, C.S Lewis says the following in Miracles (a short essay that can be found in God in the Dock, and not the same as(though very similar to) his book Miracles):

[R]ecently I saw the taunt that we Christians believe in a God who committed adultery with the wife of a Jewish carpenter. The answer to that is that if you describe the action of God in fertilizing Mary as 'adultery' then, in that sense, God would have committed adultery with every woman who ever had a baby. For what he did once without a human father, He does always even when He uses a human father as His instrument. For the human father in ordinary generation is only a carrier, sometimes an unwilling carrier, always the last in a long line of carriers, of life that comes from the supreme life. Thus the filth that our poor, muddled, sincere, resentful enemies fling at the Holy One, either does not stick, or, sticking, turns into glory.