Did I see two Milky Ways next to each other? I am from the northern hemisphere and as far as I remember, the Milky Way was "single lane", just one stripe. At least, this is what I recall the Milky Way to look like when seeing it from near Irkutsk, Siberia, in late August 1997.
Yesterday I went to Blackbutt, Australia (somewhere near 27° South, 152° East) and the Milky Way seemed to have a large black stripe in the middle.
I was wondering, if these were two spiral arms of the galaxy that we are part of.
 A: You were likely seeing what's called "The Great Rift" in the Milky Way, which is not a void in the Milky Way, but rather a cloud of dust that's "only" about 300 light-years away, and thus obscures vast numbers of stars. Last night, from Australia, it would have been very prominent in the NE in the evening sky. 
It's also possible that you saw the Magellanic Clouds, which would have been low in the South and are small galaxies that orbit the Milky Way. I don't think you'd describe these as looking like separate arms of the Milky Way, though. 
A: The Milky Way has prominent dust lanes that can obscure a significant portion of it. As seen in the various pictures in this article, there are parts where the dust lanes are so thick that it might actually appear to be two bands. I used to teach an astronomy lab where plastic celestial spheres (like world globes, but for the sky) were used. They had the region of the Milky Way outlined rather than actually printed, and in one area they actually had two bands instead of one, so you are not alone in that observation.
It doesn't have anything to do with the spiral arms. Those all overlap from our vantage point inside the plane of the galaxy. 
A: I'd rather just comment, but that isn't available to me. I think the basic cause is that the gas/dust is confined closer to the galactic plane than the stars. So the luminous region, which is composed mainly of stars is thicker than the obscuring dust. The later cuts off our ability to see stars further away, if they are too near the galactic plane. So it gives the appearance of two glowing disks that are parallel to one another. If you look at photos of edge on spiral galaxies you will see a similar effect.
The center of the milky way is in Saggitarius twenty some degrees to the south, the most prominent parts of the Milky way to observers from far northern lattitudes are further from the galactic center than the sun, and the density of dust/gas is lower, so the effect is not so great for northern observers.
