The Bradshaw Variations by Rachel Cusk is a good example of modern literary fiction. There is virtually no plot and the book looks at what goes on under the surface of the Bradshaw family life. Most space is given to Thomas, his wife Antonia and daughter Alexa though there are also chapters about Howard and his wife Claudia and the Bradshaws senior.
The motif throughout the book is musical and Thomas has taken a sabbatical from his (unspecified) job to learn to play the piano and look after his daughter. Antonia is struggling with a recent promotion to head of the English department at a university. I liked the writing style and the musical analogies helped to explain the characters. I wondered when I started whether it was going to be a bit too self consciously literary but in the end I enjoyed it and found it worthwhile reading.