There's nothing wrong with both being present in a story, but it's entirely up to how it's presented. While a silly scene can quickly turn serious to show that shit's really hitting the fan, a serious scene turning silly can really anger the audience if done poorly. It's a very hard line to correctly attribute.
It depends entirely on how the story is written, and if one scene flows into another believably. If things are jaggedly done between the two, it would come across as more akin to a Looney Toons episode than something you'd want to keep invested in viewing or reading.
The rule of thumb is to first determine what kind of story you want to write between the two, between light-hearted and drama-epic. From there, you can write your characters with some believable quirks that could lead to a silly or serious scene, and let your writing flow accordingly.http://www.youtube.com/watch?v=gfUTihyusSg
Same story, same characters, different attitude. The firstmost was just a stupid idea that made Kamina look like a dumbass in his zealousness, but it turned out to be so stupid that it actually WORKED
(can't find a scene, just trust me on this one). Then later shit really hits the fan, and it goes from "silly" to "serious" to "holy shit" rather quickly. It's all about the presentation