Does "Happy And Married" Equal "Happily Married"?

mom and dad kissing with child watching at bowling alley

We're happy and married. Isn't that enough?

A decade ago, when one of my sons was still a preschooler, a friendly old gent in the grocery checkout line tried to make small talk with the boy, who was attired in a New York Yankees jacket. 
"Oh, are you a real slugger?"
From the kid, silence.
"Are you a big strong boy?"
More silence.
Finally, winking, "Are you married?"
The boy spoke. "No, I’m happy!"
We all—everyone within earshot—laughed. My son, delighted but oblivious, laughed the loudest of all. I've never forgotten that moment. Now 16, my son can understand—at least a little—why this particular tale puts an ironic smile on people's faces when (to his embarrassment, I'm sure) I retell the story at unpredictable intervals.
I think I tell it sometimes as a personal gut check. I've been married now for 22 years and, overall, I'm pretty happy. Is that the same as being "happily married"? Or is happily married just some trite, bland expression bandied about in lame TV movies to extricate a character from a flirtatious encounter that suddenly turns not-so-innocent?
What interests me is what this particular idea means for my husband and me, and for our family. Does "happily married" translate to being two people who are each reasonably happy? Or does it mean that we are happy with the current state of our marriage? Perhaps it means that we are generally happy about being married to one another? I wonder—if asked—whether our kids, now or in the future, would describe their parents as happily married.
I know my husband and I, in sight of our children, often hug and (not too passionately) kiss. We touch one another affectionately, hold hands and walk arm in arm. Does that indicate that Mom and Dad are still in love (happy!), or just that we're really comfortable together? Sometimes, after bringing home my favorite flavor of ice cream, Frank might tease—neglecting to consider who might be listening in—"You can pay me later." Does this telegraph that Mom and Dad have a satisfying intimate life, or is it simply TMI? 
And what about the rest? When we argue over stupid trivialities and important issues (because we do), when we are overworked or overwhelmed and go days without much adult conversation (we do that, too), or once in a while when we are unusually silent and cold in order to make a point over some perceived or definite slight (okay, it's me who serves up the cold shoulder), what do the kids think then? Unhappily married? Happy with an asterisk? How To Fight In Front Of Your Children
We kid ourselves into believing that the few seriously unhappy stretches in our marriage have been kept hidden from our children. We know better, of course. We know that the kids see, hear and absorb any unhappiness that has, from time to time, infected our marriage. Maybe we ought to hide it better, but perhaps it's wise that they get a well-rounded picture of what two adults who are, overall, not unhappy look like in a real marriage.
I wonder, too, if we are showing our kids the huge, unspoken truth about the relationship between happiness and marriage: that being happy while married has a lot to do with being happy, period.
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