"They might film a new movie," implies that the act might take place in the future, though the sentence is not actually in the future tense. "They might be filming a new movie," implies that the act might be currently taking place, which changes the meaning of the sentence slightly. Switching the first sentence to the passive voice keeps the implied tense in tact. "A new movie might be filmed." A: "I really liked that movie. Is there going to be a sequel?" B: "I heard they might film a new movie sometime next year. It might even be filmed in the Spring" A: "I really liked that movie. Is there going to be a sequel?" B: "I heard they might be currently filming a new movie."

Grammatically, "They might be filming a new movie" could literally be understood as they are in process (right now) of filming a movie. It is always best to write in active (not passive) tense to achieve good grammar. Keep in mind that all languages have different registers (formal to informal). If you were to say the same sentence "...might be filming" in normal conversation, I would understand you perfectly. Writing is something quite different and calls for a higher register.

"They might be filming a movie" is in active voice, not passive. The corresponding passive construction would be "a movie might be being filmed". "Might be filming" works like "may be filming", except that using "might" in place of "may" has a connotation of more tentativeness and uncertainty. Whichever modal verb you use is combined with the continuous infinitive "be filming".