Admittedly, freezing one character on screen can be a joke, not a serious moment. I can't really think of any examples outside of sci-fi/fantasy/anime because of the strong magical component involved in freezing time like this. Here are some serious examples.
Harry Potter has the
Petrificus Totalus spell. Hermione uses it on Neville in the first film, and on the Death Eater Dolohov in the last film (well, Deathly Hallows Part 1, anyway). The frozen character has essentially no further part to play in the scene - it's like they've been hit with a stun gun. It is possible they are still aware, though.
The operative in
Serenity also manages to freeze people so he can monologue and then kill them, but in a non-magical way.
Rolo from
Code Geass is able to speak and act while others are frozen in place. This can be used for assassinations or more subtle tricks. Without the background, the emotional impact of these scenes is likely lacking - there's a lot of double dealing and deception in this story.
And there is (of course!) a Star Trek episode dealing with this. The crew of the Enterprise encounters 'temporal anomalies' that cause whatever is within them to freeze for a time. Naturally, some people are frozen and some are not. There is suspense and a mystery to unravel...oh, and if they don't figure it out, everyone dies.
Clips from
Star Trek: The Next Generation "Timescape"
Also, in the final part of
Jonathan Strange and Mr. Norrell, there is a scene where Childermass is frozen in place by the Raven King. Nobody dies!
You can see the scene play out about 10 minutes into this collection of clips. As you can see, they are intercutting several parts of the story at this point, so we keep returning to see Childermass and the hanged Vinculus while hearing voiceover from the magicians (Strange and Norrell). This is building to the climax of the film. I seriously doubt we're going to portray Melian as *ominously* as the Raven King appears here, but other aspects of this portrayal may be relevant.
What nearly all of these scenes have in common is the tension of a fight scene and/or impending death. We will....lack that tension. I think that portraying Melian as ominous or dangerous is okay to a point, but only in the sense that falling in love changes your life, not in the sense that we should have the audience thinking she's going to kill him. Avoiding making it look silly is one thing; avoiding making it boring is something else. If we portray Melian as freezing Thingol while remaining mobile herself, that will imply that she has cast a spell on him and that he is under her enchantment/power. I think we want to avoid that implication, so having them both 'caught' in the spell makes it more mutual. I think if only one person is frozen, the audience will expect the other person to do something significant in the interim. We have nothing for Melian to do, and so she should be frozen as well.