The arrangement you wish does not seem feasible.
If by "dim" star you mean a star that is dimmer than our sun, you are probably thinking of a red dwarf. Such stars are thought to be far from habitable, because:
- The habitable zone around them requires a tidal lock;
- They are usually flare stars, which means the star facing side of planets in the habitable is toast;
- They vary their luminosity a lot. Even then, it is mostly infrared. Those stars have an average surface temperature of 1700K (compare with ~5600K of the Sun).
- The proximity to the star means that the star's own magnetic field will probably overcome the planet's, meaning little to no protection from solar wind, meaning no atmosphere.
If that is not discouraging enough: if a binary system has evolved in a way that has caused one star to be much brighter larger than the other, then it is most likely a semidetached system. That's because in general bright stars are young, dim ones are old (this is a very base supergeneralization), and if two stars close to each other have different ages, they most likely have formed in different zones and are probably not orbiting each other. For them to orbit each other the younger, most massive one should capture the older one, and such captures are more likely to happen at the galactic core (because you can't capture alone, you need a third body and that's where you find a lot of stars in close space) - where excess radiation is hazardous to life as we know it. So, if two stars are orbiting each other and one is much brighter than the other, they probably formed together and evolved to be like this:
The dimmer one in this case is the one to the right. The one to the left is colder, but its sheer size gives it more shining area, and therefore more luminosity.
This does not bode well for your planet. If it orbits in a plane that allows for an eclipse, it will cross the mass transfer stream when it forms. That will either decellerate the planet into crashing onto the smaller star, or fling it away from the binary. But not without causing it to be torn apart first. Not from the collision, but due to gravity!
In your previous question about six-month periods of darkness, I gave you an answer which I think is far more feasible and which does not depend on a binary system. I think you should consider that one.