This is something I am learning how to do. It is possible.
I used to take myself way more seriously than I do now. Maybe I still take myself too seriously. But in changing this, I had to come to terms with the fact that I am, for the most part, serious, and that is something I don't want to change. I like to deal with serious questions. I like to say and do deep things. It dawned on me that I could do this without carrying the world on my shoulders.
This does not mean that I have to tackle the serious questions in an entirely serious way. In fact, humour is usually the best, and often the only, way of approaching the deepest questions.
ie:
"God is dead." -- Nietzsche.
"Nietzsche is dead." -- God.
This does not mean that I am depressed or depressing, either. I take my joy in big, deep breaths.
As Kerouac said:
"All laughter is solemn."