Putin is a realist. Ascendent militant Islam is not in Russia's short, mid, or long-term interest. Perhaps he identifies with Bush better than Kerry, since a Kerry presidency would be Clinton-redux, with many of the same players. Russians will never forget how Clinton went after Yugoslavia based on a hoax, or how he manipulated Yeltsin.
I suppose you could say they are allies, like France and Germany, though a little more important since they have more resources. France and Germany also saw fit to outfit Saddam and China, but even they aren't crazy enough to help the ayatollahs to go atomic.
With regards to North Korea, it remains to be seen what side he'll come down on.
That said, during these perilous times in Russia, Putin is probably the best man for the job. One can nit-pick him, as you can Bush, but there are really no good choices to run either country right now, other than Putin and Bush.
Putin will continue to place Russian interests ahead of US ones, as he should. When these interests temporarily coincide with ours, yippee. When they don't, vse ravno.
“Nations have no permanent friends and no permanent enemies. Only permanent interests.” - Benjamin Disraeli.