I love the idea of two stars. My Cataphant creature (which I'll put up soon) lives in a binary star system, in which a non-active brown dwarf orbits a very active red dwarf. The Cataphon planet is orbitting the inactive star but the red dwarf produces enough heat to energize the planet.
In that example wouldn't the brown dwarf simply rotate around the red dwarf but would both instead rotate around a common barycenter. Depending on the mass of both objects could this result in a very variable distance between the brown dwarf and the red dwarf, making the temperatures of your brown dwarf planet/moon also very variable. You can see a simulation of how double stars behave depending on mass relation here: http://instruct1.cit.cornell.edu/courses/astro101/java/binary/binary.htm
You clearly see that the distance between the 2 stars varies a lot. Thought live could possible adapt to this by doing a wintersleep or by moving between the north and south depending on the current temperature(like birds do).
Thought it's an interesting idea to have live on a brown dwarf it's moon/planet, maybe could the brown dwarf itself radiate enough heat for your planet or generate at least enough heat to help your planet survive the cold periods when the red dwarf is far away from the brown dwarf. Jupiter, Saturn, and Neptune already produce more heat then they receive from the sun. Brown dwarfs have 12-89 times more mass and they fuse deuterium(not sure how much extra heat that would produce).
The tides created by the brown dwarf would be gigantic(similar with how Jupiter it's tides transformed IO in an extremely unstable planet with quite constant volcanic eruptions) just like it's magnetic field. Could a planet/moon of a brown dwarf be close enough to have habitable temperatures without becoming a second IO where constant volcanic eruptions and magnetic fields make live impossible?
It is believed that there is a gigantic amount of brown dwarfs, so even if there is only a very small chance that one has a habitable planet could there still be many
We know only 10% of the galaxy it's predicted mass and some people believe that most of the remaining 90% are brown dwarfs, that's a lot of dwarfs