The Bible even states that some of heavens creatures started to have carnal relations with earthly women and things sort of got out of hand. The philistines were supposedly a product of this, thus the giant Goliath.
Well... not exactly...
NIV Genesis 1:26-27
26. Then God said, "Let us make man in our image, in our likeness, and let them rule over the fish of the sea and the birds of the air, over the livestock, over all the earth, and over all the creatures that move along the ground."
27. So God created man in his own image, in the image of God he created him; male and female he created them.
NIV Genesis 5:1-5
1. This is the written account of Adam's line. When God created man, he made him in the likeness of God.
2. He created them male and female and blessed them. And when they were created, he called them "man. "
3. When Adam had lived 130 years, he had a son in his own likeness, in his own image; and he named him Seth.
4. After Seth was born, Adam lived 800 years and had other sons and daughters.
5. Altogether, Adam lived 930 years, and then he died.
NIV Genesis 6:1-8
1. When men began to increase in number on the earth and daughters were born to them,
2. the sons of God saw that the daughters of men were beautiful, and they married any of them they chose.
3. Then the LORD said, "My Spirit will not contend with man forever, for he is mortal ; his days will be a hundred and twenty years."
4. The Nephilim were on the earth in those days--and also afterward--when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.
5. The LORD saw how great man's wickedness on the earth had become, and that every inclination of the thoughts of his heart was only evil all the time.
6. The LORD was grieved that he had made man on the earth, and his heart was filled with pain.
7. So the LORD said, "I will wipe mankind, whom I have created, from the face of the earth--men and animals, and creatures that move along the ground, and birds of the air--for I am grieved that I have made them."
8. But Noah found favor in the eyes of the LORD.
This verse...
Genesis 6:4. The Nephilim were on the earth in those days--and also afterward--when the sons of God went to the daughters of men and had children by them. They were the heroes of old, men of renown.
...says NOTHING about the N being the OFFSPRING of the SoG and the DoM: they were ALREADY there!
SoG are the offspring from the early Adam/Eve lineage and the DoM are the offspring from the LATER Adam/Eve lineage, nothing more.
NIV Numbers 13:33
We saw the Nephilim there (the descendants of Anak come from the Nephilim). We seemed like grasshoppers in our own eyes, and we looked the same to them."
EVERYTHING got wiped by the flood: there was NO WAY for these supposed 'angelic' offspring to have survived to THIS point in time.
Topics: Nephi'lim
Text: Gen. 6:4; Num. 13:33, R.V.), giants, the Hebrew word left untranslated by the Revisers, the name of one of the Canaanitish tribes. The Revisers have, however, translated the Hebrew gibborim, in Gen. 6:4, "mighty men."
NIV Jude 1:6
And the angels who did not keep their positions of authority but abandoned their own home--these he has kept in darkness, bound with everlasting chains for judgment on the great Day.
Nothing HERE about angels MATING with humans, either.