That Marthe, she was never out of the bath. It's a wonder that Pierre ever got a look in. But when he did, writes Tom Lubbock, he gave a unique view of a marriage at work
There's a statue of a faithful dog in Edinburgh, but the human heroes of private life get few monuments. What could we have: the tomb of the unknown hubby? Well, there's Oprah Winfrey et al, offering a brief pedestal to personal strugglers. But generally our heroes of heart and home are drawn from fiction and the already famous. One of the main reasons we have novels, soap-operas, tabloids, biographies is to provide such exemplary lovers, couples and families, and the lives of poets are often very good material: the Brownings, Oscar and Bosie, Tom and Viv, Sylvia and Ted, Larkin too (the emblem of a certain kind of single life). And then, from the lives of the artists, there's Pierre and Marthe.

The relationship of Pierre Bonnard and Marthe de Meligny is a curious art-life cross-over. It isn't a biographical extra to Bonnard's art. Indeed, it offers little overt drama. Pierre met Marthe in 1893, when he was 26 and she was too (though claiming and looking 16). He picked her up in a Paris street, they moved in together, and stayed together till her death in 1942, five years before his own. They married in 1925. They had no children. It's the sort of marriage that, although unconventional then, doesn't get in the papers. And, even with Bonnard's painting, we mightn't be so interested in it - if the painting itself weren't.

But the painting is. The relationship is far more than background - it's Bonnard's big subject - and to see Marthe as just the artist's model, or his "muse", misses the point. Pierre and Marthe become private-life heroes because Bonnard's art specifically makes them so. In fact, it's hard to come up with another major body of work so consistently focused on the life of two people together. (The only parallel I can think of is the work of the Victorian poet Coventry Patmore, one long celebration of his own married life, but the likeness is remote.) So it's as well that the Tate's current Bonnard retrospective is a big one. You need to see how the subject never goes away - the sheer number of pictures that concern one man and one woman, their cats and basset-hound, the places and the rooms they lived in - and how, through a 50-year span, the painting handles the relationship.

In the show's second room, the liaison is in its early years, and the pictures make one clear assertion: we're having lots of sex - a difficult thing to advertise gracefully to the world, though one sometimes wants to. Look at Indolence (1899) - with Marthe sprawled naked, supine, post- coital on a rumpled bed - and imagine coming across a comparable image in someone's photo album, how you'd think "I probably wasn't meant to see this one" - or "I hope I wasn't" - because that sort of erotic showmanship would be rather nauseating. And, with these Bonnards, it is a fine line. He doesn't convert his sex-life, like Picasso, into general sex-symbols. It's definitely this particular woman on show. But Bonnard saves the gambit through an intimacy so absorbed that it becomes un-selfed. The viewpoint is clearly his, him standing by the bed looking down, but before him Marthe is lost, in herself and in the sheets that fold her body into their light.

There are no more such bedroom scenes after the early 1900s. But the point shouldn't be over-stated: the paintings are not a confessional documentary. They don't tell tales. The internal drama of the marriage is conveyed obliquely, and must to an extent be read in.

Take the many pictures of Marthe bathing. One way, they look like variations on an established theme, the "Nude in the Tub", and that's how Bonnard titles them. But evidently it is the same woman, and the same woman who appears clothed in so many of the interiors; and Pierre himself is present in these bath scenes, indicated by an intruding leg, or again just by a viewpoint - the viewpoint of someone who's in the room too, and close by. And when you know that Marthe, due to some mental or physical complaint, spent hours daily in the bath, the repeating subject becomes more than a theme. The bath seems a refuge or a prison, and you wonder if this was a marriage of great convenience for an artist who wanted to paint bathers - or if bath-time got as obsessional for him as it did for her.

Criticism of Bonnard's art easily becomes criticism of his marriage, and I don't see that this can or should be avoided, so long as you grant that marriage-criticism is at least as tricky a practice. Naturally the art only gives one side of the relationship (but that's an exemplary role too: all anyone has of their relationships is a one-sided view; how you deal with that one-sidedness is the issue). And then the paintings, with their saturating colours and sensory plenitude, seem to say it was all bliss, a paradise - while the facts suggest it must have been miserable, or miserably unequal, a sorry sort of shut-away mutual bondage, with her (on some accounts, basically a nutcase) wholly dependent on him, and him a dubious martyr, needing and nursing and using her dependence.

What does that do to the pictures? Make their intense plenitude claustrophobic, or the sign of an all-infusing, all-transfiguring love, or a resolutely denying and thriving fantasy? Perhaps rather an intimacy and habituation that can hardly tell the difference between these things. Marthe is everywhere, visible and invisible. Bonnard deals in Mary Celeste still-lifes and interiors, which carry a human presence even when there is no person there, and in a kind of picture puzzle - there is a woman concealed in this scene, can you find her? - where Marthe either lurks inconspicuously but insistently, as a dim profile just inside the painting's margin, or is incorporated so thoroughly into the colour scheme that her figure, though central, is barely discernible.

Sometimes he has both effects, Mary Celeste and "Find the Lady", together. I was looking at White Interior (1932) for a while, thinking "How's he done it? How does he get such a strong feeling that someone has just gone out, and will shortly return?" - something to do with the relationship of the orange chair and the white door - and then I saw that she was in fact there, nearly in the middle of the picture, but hidden by the way, bending behind the table to play with a cat, she virtually blends with the carpet.

Bonnard famously said he wanted his paintings to give the impression of someone just entering a room, an optical overload, more than can be taken in at a glance. Here that's just what happens. You go through the sequence thinking first "She's definitely around somewhere", and then "Ah, Marthe, there you are!" - or more coolly "Oh, there she is". For Marthe's pervading presence needn't be felt as a simple blessing; maybe as inescapable. Always around - that can be said in several tones of voice, and paint. Bonnard paints her in so deeply that he almost paints her out, and thereby shows that paint her out, he can't.

When Bonnard is alone, in his self-portraits - if you can call them that, because they're always the view in some mirror in the home, a moment of reflective solitude, not a set-piece self-image - he seldom looks happy. In the one called The Boxer (1931), you see a puny man beating his fists in a tantrum. In one of the last, after Marthe's death, Self-Portrait in the Bathroom Mirror (1946), he looks like a dead man himself. And the late bath-scenes, painted before and after she died, are rather frightening fantasies.

Marthe's body never ages, but it acquires distortions that neither water nor a wide-angled view can explain. It floats corpse-like, it dissolves into its liquid cocoon and into the painting; in the last one of all, into a sea of sour metallic hues no one would call paradisal. One hardly likes to speculate what mixture of grief, remorse, nostalgia and resentment is to be fathomed here. An exemplary marriage: an abyss. The only clear image in this final picture is the basset, heraldic on a bright square of bathmat - as if to say, the man may be lost, but the dog at least is simply faithful to the woman's memory.

To 17 May, Tate Gallery, Millbank, London SW1 (0171-887 8000)