I'm designing a handbill that has a sort of poster/cover image on the front and then event details on the back. I've been able to lay out the details in a more pleasing way on the back if I have it in landscape orientation, but I'm worried that it will look sloppy if the front is portrait and the back is landscape... or is this something that people do all the time anyway?
A handbill (or a flyer as I'm used to call it) is given by hand and read in hand: everyone is used to look at the both sides of the flyer hence they are used to "operate" the flyer. So: rotating the flyer is not an odd action for the holder to do.
Compare to e.g. a poster which is always read from a fixed position and can't be "operated" (ie. turned, rotated). If the viewer wants to change the orientation of the poster heshe must rotate hisher head instead — which is an odd action to do in this context.
Furthermore, it is more okay to layout the info on the handbill how it can best be laid rather than cramping the data to a fixed orientation. The flyer-viewers are much more pleased to use their hands to rotate the flyer rather than using a microscope to read the info or figuring out why the info isn't laid in a logical structure.
Sometimes I've even had the upper half oriented differently than the lower half, because that's how the given info fitted less cramped. This, of course, should be done with the overall style in mind: I've done this to a rock festival's flyer where a little chaotic feeling is only positive. If you want to express a tranquil feeling of an opera house, maybe better keep just one orientation per one side of a page.
Another note on splitting a page to two orientations: the flyer's size was A5 — therefore it was highly probable that it will get folded, so, in real life use, it probably wasn't that chaotic after all.
An excellent question, and a great answer from koiyu.
I'd add to what koiyu said that it's never optimum to have different orientations, front and back, but it's acceptable where you have no choice because of image format and copy constraints, on the rare occasion when the subject lends itself to a slightly oddball treatment, or (rarer still) where the two sides are basically standalone handbills that happen to be on the same piece of paper.
For a handbill, specifically, I always opt for vertical orientation when I can, because it's easier to hold and read than landscape at normal paper sizes. Anything that must be landscape goes on card stock if I have any say in it. (I'm not shy about having my say...) For a postcard there is a different set of considerations. What's here is strictly about handouts.
Here's how I make the call:
If the back follows from the front (for example, a teaser on the front like "Did you know...", with the rest of the information on the back) I will go to extreme lengths not to change the orientation. It's jarring to the reader and reduces the marketing impact. People throw stuff away really, really quickly, just as they'll navigate away from a web page if anything doesn't "feel right." In my observation, it more than doubles the "throwaway" rate. You'd be amazed to watch people in a crowd look at the front of a handout, flip it over, then throw it away rather than turn it sideways to read it. Try it some time. I guarantee it will be an educational experience!
Sometimes a key image requires landscape orientation. In this situation I'll try to keep front and back the same, but am willing to compromise to gain readability. Here's an example of a rush job where landscape was the only way to go. This ended up smaller than originally conceived, and on card stock.
One way to avoid portrait/landscape problems that can work very effectively is to run a huge headline sideways, like the "Student Special" in the example. Sometimes that can let you put all the needed info onto one side of the handbill, like this one for the same client. I convinced them that it was better to send people to the website or the box office, rather than clutter up the back with a bunch of detail. In a handout, less is always more: