Yes it's definately possible. You could think of it as having your head in the clouds but your feet on the gound. Being way out there and totally realistic at the same time. I would describe myself like that, but I could be wrong.
How? That's the tricky question because it's different from everyone. The answer however is a rather simple two words: Awareness and Wisdom. Being aware of the world, and having a look at what's going on around you will keep you more grounded. You don't even need to figure anything out either, just being observant without judging is all it takes. As you do it more and more, the majesty of the world will unfold and the "dreamworld" that you find yourself in will reveal itself to you in reality. It's a rather sobering experience actually. Dreams become real and reality becomes a dream, there's really no gap between them anymore, and it's better than either of them seperately.
As for Wisdom: Just learning the truth is what it takes. You will see the patterns that run the world, and everything will make more sense. This will help relieve your stresses too. Sometimes people experience the unreal, because what is real is too confusing and mysterious to be dealt with. Learn about the world from your own experiences and the experiences of wise people.
Through awareness and wisdom though you can find that peace you seek, and also be able to live in both worlds at once. I wouldn't say it's easy, but I would definately say it's worth it.