A Disobedient Girl by Ru Freeman. A bit like A Thousand Splendid Suns but much better IMO.
A Fine Balance by Rohinton Mistry. Some readers find this book too harrowing but I finished it with admiration for the strength of human spirit evinced by the main characters.
Brick Lane by Monica Ali. Different in that most of the novel is set in England. The story of a Bangladeshi girl in an arranged marriage to an older man.
Small Island by Andrea Levy. Set just after the war - Gilbert and Hortense are Jamaican immigrants trying to make a new life in London.