And I thought Melancholia was depressing. (spoilers)

I never really viewed this as "depressing." It's kind of like a 'it is happening, why dwell on it?' situation if that makes sense.
I think you've described the ending really well with "sad, yet beautiful" because it does seem odd that we are following these characters whilst knowing that they're going to die so soon. Almost to the point where you hope that something miraculous does happen and they get to spend their lives together. Though I agree, that would be a terrible ending.
But quite frankly, them finding someone that feel happy dying with is one of the most beautiful things in the world. Living on gives the possibility of breaking up and being lonely all over again. Here, they're dying happy. Surely dying happy is the ultimate goal. Dying is an inevitability, we all need to find that one person who can make us smile as it happens.
The final line of the film too; "I'm really glad I got to know you" is beautiful in itself, as he earlier said; "I just can't spend the last month of my life getting to know someone." I think the idea that one person can have that sort of an impact on you is a really nice thought.

I agree that this was by far more depressing than Melancholia, but I also kind of think it had a more realistic approach. Like there are a lot of little incongruities that could make it unrealistic (like the flying a little Cesna to England), but it deals with more people and has a wider perspective.

I liked Melancholia, but it's more disconnected from real life. How many people can really relate to living in a fancy manor secluded from all society? And to people who have no experience with depression, the beginning can be alienating.

Agreed. I watched this movie a few times, and though the whole premise is comical, I couldn't help but feel a bit dejected towards the latter part of the film. Dodge and Penny's journey was fun to watch, but the ending was hard to make light of. First, I couldn't help but think of how sad it was that Penny turned down the chance to see her family for Dodge, who is ostensibly a stranger. And it was sad to see their relationship cut short when they were clearly still getting to know each other. Dodge was still learning things about Penny by the very end of the film (asking about her family, siblings etc) which goes to show how untimely the whole ordeal was. They exchange a few heartfelt words and then boom. I'm bummed just typing about it.

Melancholia wanted you to know right from the get go - that the movie would not have a happy ending. The entire movie, aside from the fact of dealing with the end of the world deals heavily on depression (director stated that in a Q&A). Per the movie, there is nothing happy, charming or gleeful about spending the last hours of your life when dealing with depression.

This movie was refreshing. And even though from the get go you knew the world was going to end, it was all about finding that bit of happiness, charm and gleefulness before the end - and finding it with someone you love. I loved every single minute of it.