The Maskil LeDavid on Bereshit 8:22 says that even though the sun did not rise or set Noach had signs to recognize and distinguish between day and night, since he needed to know this for many reasons. Also, not all the animals ate at the same time, and Noach needed to know when to feed the animals.
According to this we can say that the dates were marked by the passage of time (i.e. 24 hours was one day) rather than by the sun's rising and setting.
This is reminiscent of a story that is told about the Ba'al HaTanya when he was imprisoned for the first time:
Once, for instance, the Rebbe was put into a room which was as dark during the day as it was at night. A small lamp was the only source of light. One day, about two hours after noon, the Rebbe was told that the time is already past midnight and he should go to sleep.
"Right now," retorted the Rebbe, "the time is two hours and five minutes past noon."
When asked how he could possibly know such a thing, the Rebbe explained.
"Every day is illuminated by the twelve forms of the letters of in Ineffable Name (Tetragrammaton), while the night is illuminated by the twelve forms of the Name denoting G-d's Lordship. By experiencing these various forms I know to distinguish between day and night, and between one hour and the other."
Also, the Mabul lasted a complete solar year (Rashi Bereshit 8:14), so everything would have picked up right where it left off. (Although this doesn't explain the 11 day discrepancy in the lunar calendar)