The viewer is shown a realistic version of what happens after courtship and marriage, the idea being that you don't just marry your spouse, you marry their whole family. While it is implied that a parent's blessing enhances a romantic relationship, Shrek 2 proposes the idea that preserving a marriage is more important than dissolving it to satisfy a selfish parent. In this case, King Harold works hard to get Shrek out of the picture so that Fiona can wed Prince Charming, but Fiona decides to stick with her ogre husband, and the "ugly" couple's happiness seems to reinforce the belief that it's what is on the inside that counts, and physical looks shouldn't matter. The third Shrek movie continues the natural progression of Shrek's adult life. After falling in love and getting married, then meeting the in-laws, Fiona expresses in Shrek the Third her desire to someday have a family. Shrek is quite taken aback and protests that he would be a bad father. In addition to this dilemma, Fiona's father passes away and leaves Shrek with the choice to either find the long-lost heir or assume the throne himself. Since Shrek has absolutely no desire to serve out royal duties, he vows to set off with Donkey and Boots on a quest to find the late king's distant relative, Artie. At their ship's departure, Fiona informs Shrek that he is indeed going to be a father, and Shrek begins to have serious (but humorous) nightmares about baby ogres disrupting his simple life with Fiona. Shrek is terrified of becoming a father since "No one ever says, 'Sweet as an ogre,'" but gradually begins to warm up to the idea. After finding Artie, he begins to get some fatherly practice relating to the young difficult teen. Artie talks about the struggle of growing up fatherless, and Shrek shares some of his own problems as a young child in relation to his father: "My father tried to eat me." We see how much positive change has occurred in Shrek's individuality (thanks to marriage and friendship) when the ogre encourages Artie to "be your own man, ignore...

"Just because people treat you like a villain doesn't mean you are one," Artie says. "The thing that matters most is what you think of yourself." Under Shrek's nurturing and influence, Artie appears to grow from being a difficult, somewhat timid teenager to a young man who is self-assured enough to be the future king of the land of Far Away. At the end of the movie, both Shrek and Fiona are shown sharing the tasks of raising their three baby ogres. Donkey also has offspring in the third movie (half dragon, half donkey) and is shown being affectionate with them. A third example of parenting is shown when the Cyclops guard says of his daughter, "Who would have thought a monster like me deserved something as special as you?" As for the main character, Shrek's fear of becoming a parent seems to dissipate throughout the course of the movie, and he settles into the role of fatherhood just as sweetly as he has that of husband and best friend in the previous films.
Although the Shrek movies do contain crude humor, language, and even some sexual references, the basic family themes are still there. The fictional marriage and family interaction of the animated couple are displayed with themes that can be applied and understood in real-life relationships.

Sources

Adamson, Andrew and Vicky Jensen. Shrek. Mike Myers, Eddie Murphy, Cameron Diaz, John Lithgow. Dreamworks, 2001.

Adamson, Andrew, Kelly Asbury, and Conrad Vernon. Shrek 2. Mike Myers, Eddie Murphy, Cameron Diaz, Julie Andrews, Antonio Banderas, John Cleese, Rubert Everett, Jennifer Saunders. Dreamworks, 2004.

Miller, Chris. Shrek the Third. Mike Myers, Eddie Murphy, Cameron Diaz, Julie Andrews, Antonio Banderas, John Cleese, Rubert Everett, Justin Timberlake, Eric Idle. Dreamworks, 2007.