I work for the Canadiens and I´m asked that question all the time. I can unequivocally say that the CH stands for Club de Hockey and doesn´t refer to either Canadiens or Habitants. The same logic applies to the old CA logo which they wore in the early years. In that case the CA stood for Club Athletique.

I don´t think anyone disputes that The Canadiens are called The Habs because of their origin as french canadians called les habitants. The Canadiens as a team has evolved over the years and so has their jersey. When the club was born in 1909 they were simply the "Club Canadien" with just a "C" on their jersey, then in 1911 they became "Club Athlétique Canadien" with "CAC" on their jersey, for 1914-1915 season it changed again to a large "C" with a smaller "A" within the "C" (which was their uniform when they won the cup in 1916). By the next season, the Club Athlétique Canadiens was no longer in business, the "A" changed to "H", the new "Club de Hockey Canadien" was born, and the uniform has remained essentially unchanged ever since.