It's OK.
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.