I might have mentioned in the comments of my first post on this here blog that I'm a huge fan of Questionable Content. It's a great comic with a healthy dose of humor, character development, and music. Granted, I don't understand most of the music jokes they make, it is still not an alienating aspect. But this is not the comic I am recommending. A comic that I found through this comic is called Anders ♥ Maria.
It is the story of two lovers that go through the trials and error of romance. Theirs is a story of love that is anything but perfect. It gives one a look into the gritty aspects of human relationships that aren't always talked about. Reading this comic is frustrating at times because the characters do so many stupid things. Yet it's this aspect that is so endearing. No one is perfect, and everyone does stupid things.
The humor in this comic ranges anywhere between witty one-liners, to incredibly black comedy. It gives the reader a view of the funny things in life that one doesn't usually find so funny. It was infuriating keeping up with this comic, because the author Rene Engström was very volatile with her updates. But now that the comic has concluded, I wholeheartedly recommend you check this comic out.