A source told the New York Daily News newspaper: "They had a huge fight, and
they're not speaking."
Michelle reportedly snapped at a reporter who asked her to comment on her
relationship during New York fashion week.
Despite the reported problems, the couple attended the Independent Spirit
Awards and the Oscars together.
Heath, 27, and Michelle, 26, have a 16-month-old daughter, Matilda Rose.
In January, the couple fuelled rumours they had secretly wed after they were
seen wearing rings on their wedding fingers.
Last November, they collected a marriage licence in Brooklyn, where they own
a town house in Cobble Hill.