FAMILY HAPPINESS By Laurie Colwin. 272 pp. New York: Alfred A. Knopf. $12.95.

POLLY SOLO-MILLER DEMAREST is one of those heroines of American fiction who appear to have everything. She is married to a large, handsome, usually amiable husband, Henry; she has two sweet children, Pete and Dee-Dee; she lives in a Park Avenue apartment; she has graduated from a good school and holds down a high-level job, as Coordinator of Research in Reading Projects and Methods for the Board of Education (''This job combined some of the things Polly held most dear - service, children, and books'').

What else does it take to make life perfect? The wonderful job only takes up three days of her week. Her husband makes more than enough money. Polly herself is beautiful, still young and powerfully cheerful. And she is a functioning part of a larger family that gathers together for big occasions and small - what a rarity!

The extended Solo-Miller family consists of her father, Henry Sr., who dwells in what Polly thinks of as ''the realm of the higher mind''; that is, his mind is on his own concerns. Polly's older brother, Paul, is a priggish bachelor whose reputation for intelligence is so firmly entrenched that he no longer has to say anything bright. The younger brother, Henry Jr., has married the daughter of Czech refugees: ''She and Henry, Jr., behaved more like brother and sister than like a married couple. They wore each other's clothes, did not plan to have children, played with their dog, and dedicated themselves to kite flying.'' The chatelaine of the extended court is the former Constanzia Hendricks, now called Wendy, a wellbred narcissist who has trained up her daughter, Polly, to be her perfect luncheon companion. Polly's place in the family is clear: ''She had never given anyone the slightest pause. Her family doted on her, but no one felt it was necessary to pay much attention to someone as sturdy, upright, cheerful, and kind as she.''

The situation, then, is perfection to start. Readers of Laurie Colwin will remember that her last novel, ''Happy All the Time,'' ended with just such a portion of domestic bliss: plenty of order, harmony, civility, good meals; plenty of champagne, good-looking young men and women in love and the implicit promise of a new generation. But ... then what? Polly used to be in love with her husband, but Henry is a good provider, which means he spends a great deal of time at work and often is too tired to make love in the evenings or jokes in broad daylight. So Polly is in the position of a person who has bought a gorgeous car that doesn't run very well: It looks good (people express their envy to her constantly; they're convinced she's got life ''aced''), but she knows that under the hood the motor's a lemon. The beautiful husband won't talk, the children are ephemeral, and the family that functions as a fortress for her is also, of course, a prison.

It will come as no surprise that Polly takes a lover. What else can she do? Not for her Peru, or the Peace Corps, or a Ph.D. It's a lover or nothing. Hers is out of a dream. He's well educated and from her class - a painter whose work and temperament dictate that he spend most of his waking life alone. His name is Lincoln Bennett, and he's madly in love with Polly. ''Family Happiness'' consists of the question, how happy can family happiness make you? Is it all right to want a little of your own happiness? Can a female human being expect to be seen as a human being instead of a family functionary - a robot who picks up the baguettes for a dinner party, who takes her husband's business suits to and from the cleaners, who can always be relied on ''to provide something scrumptious for dessert''? In many ways ''Family Happiness'' seems like a charming, ingratiating, beautifully written novel saved up from 50 years ago. Certainly the Solo-Miller family comes from predivorce days. Polly seems never to have heard of the feminist movement in any manifestation, and her moral scruples seem exaggerated for any decade of the 20th century. She is afraid to have Lincoln visit her at her apartment for even a ''social'' call, because she is afraid of what the doorman will say. Polly and Lincoln's affair continues. Her family never notices because they never notice her. But her early euphoria turns to guilt, gloom, despair. She and Lincoln separate for a while, and Polly, driven by this series of devastating emotions, finds a girlfriend to confide in at her office, begins to talk to her husband again and - for the first time in her life - rather petulantly sasses her mother. After consolidating these gains, will Polly return to the straight and narrow, or will she keep her handsome, attentive lover?

This is ''women's material'' with a vengeance. But then what do most women have but marriage and children? How do they express freedom, despair, rebellion, mutiny, euphoria, abandon, except with a lover? It is certainly not Laurie Colwin's fault that these facts continue to pertain. It may be her fault, however, that the two men in Polly's life are cut from the purest cardboard. It never occurs to anyone, not Polly, not any of the in-laws, not even the author, that when Henry Demarest is on a business trip, he's on anything but a business trip. He's a large, boring, nice husband, period. And the ''fact'' that Lincoln Bennett, the other man, has to be alone - why does Polly believe it so implicitly? Why is the world famous painter so gaga about this sturdy, cheerful housewife that any other woman is out of the question for him? Because he must function here as part of a housewife's fantasy, that's why.

SOMETHING'S wrong with the story of ''Family Happiness.'' Polly is so much a compendium of secondary virtues that she doesn't quite appear as a human being: ''In the supermarket, Polly harangued herself. People who shopped on Sunday were people who had let things get out of hand, who paid no attention to detail, who let themselves get lost. There were people who actually bought their vegetables at the supermarket.'' All this is very well in the way of scruples and refinement, but why won't Laurie Colwin let her Polly consider for a second what might happen to the rest of her life if indeed the doorman did let slip something to her husband, or if, in some other way, the world discovered the cheerful housewife was having a serious affair?

People might get hurt, the situation might get out of hand. Such a new situation might approximate reality, but ''Family Happiness'' is safe in the realm of domestic fantasy; safe -safe as houses. Which is not to say that Laurie Colwin's next novel might not deal with just this problem.

Illustrations: Cartoon