The poor doomed Waynes, parents of Batman and the beloved and equally-doomed Flying Graysons.
Flashpoint arc shows a severely disfunctional relationship because in this timeline Bruce was killed in Crime Alley. Thomas became a Grim Dark version of Batman and Martha dealt with it in ... a different way, becoming that timeline's Joker. Even with this nail it's clear they still have strong feelings for each other.
Superman and Lois Lane from 1995 to 2011. The only thing strong enough to break this marriage was a universe-wide reboot.
ElfQuest has a lot of happily married couples, despite the elves' open sexuality. Among the elves there are Redlance and Nightfall, Strongbow and Moonshade, Woodlock and Rainsong, and Cutter and Leetah. You could also add Bearclaw and Joyleaf - they do have some pretty fierce quarrels, but always make up afterward. Also the trolls Picknose and Oddbit (really!) and the humans Nonna and Adar. In the event of romantic rivalries, forming threesomes is considered a perfectly acceptable, if relatively rare, solution.
What's more, in a sense Cutter and Skywise are "married" - yeah, they're both guys (though remember, in ElfQuestEveryone Is Bi) but in many respects they act like a married couple.
All of which is not surprising when you remember that ElfQuest was created by Wendy and Richard Pini, who've been happily married for over three decades.
There seems to be a tradition of this in the Flash legacy; see also Wally West and Linda Park, and Jay and Joan Garrick, who have possibly the longest-standing marriage in the DCU.
Retconned out in the New 52. Now Patty Spivot is the third point of a triangle, and the one Barry's actually dated.
The Hawkmen and their partners (both at work and at play, as it were) used to have a similar happy relationship. Pre-Crisis, Carter and Shiera Hall of Earth-2 were married for about the same length of time as the Garricks, and used to go off on archaeological expeditions together in between JSA meetings. Likewise on Earth-1, Katar and Shayera Hol were married right from their creation. Post-Crisis (and post-John Ostrander and Hawkworld), Hawk continuity is just a mess, but Carter and the new Hawkgirl still get together fairly often. In fact the very first Hawkman and Hawkgirl's corpses are the central power battery of the Star Sapphire Corps (who are fueled by the Power of Love)
Peter Parker and Mary Jane until the One More Day comic. They're also married in the newspaper strips, and have now gone past the twenty-five year mark. This is parodied in Ultimate Spider-man, in which Mary Jane and Peter are so close that Liz Allen starts to refer to Mary Jane as "Mary Jane Watson-Parker" because "You two are totally married!" Peter even tells MJ at one point that when they become old enough he would marry her.
Likewise in Spider-Man, Uncle Ben and Aunt May had a long, happy marriage.
Fantastic Four: Reed Richards and Sue Storm-Richards tied the knot in Fantastic Four Annual #3, back in 1965, and they've been together ever since despute bumbs. Namor (among others) has had an on-again-off-again Stalker with a Crush thing on Sue for a long time, and it hasn't always been completely one-sided.
Mystique and Destiny, Rogue's adoptive parents, had an amazingly long loving relationship that began when the two women met in the 1890s and only ended when Destiny gave her life so that Mystique could live. Although it is known that through some unexplained circumstances they were separated for unspecified times, there was never seen a cross word between them. Pretty good showing, especially considering they're both villains.
The Hulk was this at the end of the Planet Hulk storyline with his new queen, Caiera.
In The Authority, Apollo and Midnighter. Interesting in that they're both gay superheroes who are happily married.
Frequently played with, too, as they still have squabbles, and the kid-equals-stability thing was utterly subverted in the Revolutions arc (though that was mostly down to Manipulative Bastard Arch-Villain Bendix). However, they've been together for a long, long time, and no matter what crap gets thrown at them, their relationship is consistently a very loving one.
Archie's parents, Betty's parents, Jughead's parents... even Veronica's parents, despite being mbillionaires, aren't using that money as an excuse to become a stereotypically disconnected rich couple.
Reggie may be a jerk, but he can't blame it on a dysfunctional family.
The only exception was Midge crying because her parents were on the verge of divorce and even then she said they would stay together "with counseling".
This is such a major point in the Animal Man comics that it affects his costuming. He adds a denim jacket over his regular skintight costume so he can carry around his keys and notes from his wife. He's the only superhero with "bring home milk" on his crimefighting agenda.
Hulking and Wiccan are well on their way to filling this trope. They're already the longest-lasting couple on the team.
Same goes for Karolina and Xavin over at Runaways as of recently Xavin was Put on a Bus. The six couple that make up the Pride also count - while they're all murdering, thieving supervillains, their marriages and family lives are quite healthy (except for the way the Steins treat Chase).
In Fables Beauty and Beast definitely qualify, despite the occasional bickerings (as Beauty points out, you can't expect a marriage to last for thousands of years without quarreling). Snow White and Bigby also qualify later.
Swedish comic book Bamse has the eponymous character happily married with four children.
The Legion of Super-Heroes: Lightning Lad and Saturn Girl, they were long-standing sweethearts since the Silver Age and the second couple to be married. When Saturn Girl became pregnant with twin boys, she was the one who decided to go back on active duty while Lightning Lad chose to stay at home to look after the boys as a House Husband. Their status as happily married was briefly undone during the tenure of Geoff Johns as writer for what was considered the original Legion, with Saturn Girl trying to keep her husband under control while he kept snapping at her for never taking his side. When Paul Levitz came back as Legion writer, Garth's anger was toned down and the Ranzzs have gone back to being a supportive couple, this time with both of them retiring from active duty to raise their boys on Garth's home planet Winath.