Is his paternal DNA the same as my father’s maternal and paternal DNA? We joined in the National Geographic/IGM Genographic Project to see whereabouts we come from; I am a female so my options were limited to maternal line. His kit showed his/our paternal haplogroup to be the really common R1B. Does that mean it’s a combination of our dad’s maternal and paternal DNA? Or just paternal? I think it’s a combination of the two, since we’ve always believed my dad’s side to be Russian and this haplogroup has not much presence in Russia. I realize I’m analyzing under ignorance and good ol’ confirmation bias, so I hope a Doper with some Mendelian expertise comes by.
Paternal haplogroups are assigned based on markers found on the Y-chromosome. The Y-chromosome does not undergo recombination with other chromosomes (oversimplification), so it’s inherited intact from your father. Your brother has your father’s Y-chromosome, who had his father’s Y-chromosome, who had his father’s Y-chromosome, and so on. Mutation events aside, you can draw a line of descent all the way back to the “Y-chromosomal Adam”, the last common ancestor of all males on Earth - or at least their Y-chromosomes.
I’ve known people from Ukraine (where I was born) who have haplogroups common to India, of all places. That’s life. 
If the R1b haplogroup has no statistical population in Russia, what that means is that any Russian genetic heritage on your father’s side would likely have come from a maternal ancestor.
The tracing of male lineage can only be done reliably through the Y chromosome, which is passed on from father to son without any recombination from other genes. Remember, men can contribute an X or a Y to their offspring, determining genetic gender. Women only contribute an X, which may be either of the Xs they posses. All other chromosomes are a mix and match of both parents, and as such, genetic material from one ancestor, male or female, may not be transmitted from one generation to the next.
Also, remember that the haplogroups are talking about populations of people over time. It’s completely possible that your father had a male ancestor who was originally from western Europe, but moved to Russia and had male offspring there. So long as the male line was unbroken, they would have carried the R1b haplogroup without alteration for a generation or three until a male descendant of the male ancestor who moved to Russia then decided to move away from Russia.
The mutations that lead to haplogroups are infrequent and may take millennia to develop. A few misplaced generations would not necessarily be noted on the Y chromosome.
Also, don’t forget to check your mitochondrial DNA, which could (and probably will) tell a completely different story.
That test is done and NG is going to post the results soon, I hope. Likewise with hubby Tripler’s X & Y. This is such an exciting project for us, I can’t even tell you.
My mom’s from Kentucky, her family’s been here since 1793 so I expect some Euro-mutt results.
Many thanks to Crescend and phouka, that was exactly the information I was looking for!!