During the period 1933-1995 from the 73rd Congress to the 103rd Congress, a total of 62 years, the Dems controlled the House for 58 years. We are now entering another long dry spell for Reps as demographics and our failed immigration policies are combining to make the Dems the permanent majority party.
Turns out we were both a little off. The Republicans gained majorities in both houses for the 80th Congress (1947-49) and the 83rd Congress (1953-55). In each case they lost those majorities after two years. Except for those two brief periods, the Democrats did hold the House of Reps for the whole time period you cite, and the Senate for the same period, minus the first six years of the Reagan administration.