No, the point of biplanes as a military vehicle was that weight being equal, they had a lower wing load than a monoplane, which means a lower stall speed and a tighter turn radius. This is in turn crucial if the dogfight is made of a slow, tight spiraling course that will bring your aircraft on the tail of the enemy.
But the bomber doesn't need this maneuverability, so it can go mono. And by doing that, you get (in the 1930s) bombers that are actually faster than many earlier biplane fighters. Which kind of kills the concept of the fighter, if it can't catch the bomber up.
The way to keep biplanes in service as the main design for military aircraft is that nobody designs a fast monoplane bomber. Maybe everybody goes for the gigantic bomber. Its defense is not speed, a higher speed than the biplane fighter; it is size itself, with lots of defensive MGs and gunners, and redundacy (say 6+ engines, and, of course, 2+ wing planes). It is big, with a big payload, but slooow. Thus you can retain highly maneuverable, but not terribly fast fighters - and they will be biplanes.
That can hold true for some time. Then somebody will come up with a smaller (and, significantly, cheaper) bomber; much smaller payload, but so fast the fighters can't overtake it.
And that's the end of the biplane fighter too.
Just as wonderfully anachronistic and absurd as, say, a nuclear-powered steam train...now there's an idea for the photos from alternate worlds thread... or for a continuation of your British Transport (or whatever it was) timeline, Dean?