Yes, the point of most sitcoms is to follow the lives of a group of people and therefore they often have some drama scenes. In Friends, the whole storyline about how Monica and Chandler couldn't have children wasn't that funny at all (well they explored the comedy value of it after, but when they found out, the tone was definitely dramatic), and was handled very well.
I'm not quite convinced by all the drama in HIMYM, especially cos I think most of the cast are very mediocre actors. Marshall's dad's death didn't affect me as much as it should have, and I think it was due to the very wooden performance by Jason Segel (and I say this even though I really like the actor).
I'm quite bored by this show now, but I've watched so many episodes, I intend to watch it til the end. It's only 20 minutes a week after all.