Fred and Faye MacIntire, Davan's parents from Something Positive. Faye dies peacefully of old age, and since most characters are based on the cartoonist's life, his mom started looking at him funny. The strip after this had the tagline at the bottom: "I got a very annoyed voicemail from my mother today. I wonder why?"
Also Aubrey and Jason; they are also based on real people, though those people are not a couple in real life.
Donovan and Miranda Deegan in Dominic Deegan who still get busy every once in a while.
Zoophobia's Alanzo and Jackie are a married couple who are frequently described as "completely inseparable soulmates". They also style their hair after each other.
The Dunkels from El Goonish Shive have a peaceful, happy home life. It's made sweeter by a small panel's implication that Elliot was a mistake that happened too early, but they soldiered on through the hardships.
Fox and Collin of Friendly Hostility. Fox's parents (and Rafi) have been happy together for decades.
In Fans!, Rikk's parents are happily married. Later Rikk's marriage to Alysin proved to be rather tumultuous (Aly's tendency toward self-loathing led to her wanting to break it off with Rikk at one point). Rikk and Aly (and Rumy) are a happily married couple triple.
Erika and Matt of DAR: A Super Girly Top Secret Comic Diary, both in the webcomic and in real life. Erika herself says that her years with Matt have been the happiest time of her life. Made even more noteworthy by her originally being a 100% lesbian with a very dim opinion of "hetero-normativity" until she met Matt.
In PS238, Malphast's parents are quite happy together, although, given they're personifications of Chaos and Order, it's not entirely clear if they're actually married. But if they were humans, they'd probably be a model family.
Mr. and Mrs. Cake from Slice of Life, just like their cartoon counterparts. They shamelessly refer to each other with cutesy nicknames in public, and never get angry or frustrated with each other, even when dealing with their more troublesome customers or suppliers.
Mrs. Cake: "Well, let's get this over with, ginger-beer." Mr. Cake: "We should probably knock, sugarpie." Mrs. Cake: "Oh, one of us should, toffeebean." Mr. Cake: "Sometime soon, fizzypop."
Commander Vora and her husband General Lagan from Art Of Domination had been married for 20 years at the start of the story, and are very much in love.