Has a commercial or military jet bi-plane ever been manufactured?
Yes

I present to you, the Belphegor, a jet powered, crop-dusting, biplane. I think I need not say that this is a Soviet Bloc design, from Poland in particular.



Note the braces between the wings acted as tanks for whatever chemical agent it would be dispensing over the kolkhozy. It was not very successful due to a host of disadvantages, including:


Jet engines are not efficient at slow speeds, which are in turn required for crop dusting operations. The designers may have hoped to do away with this requirement by using it over the large collectivized farms of the USSR, but the straight wing attests to the top speed being low by design. The jet engine was apparently mandated by soviet planners wanting to simplify the logistics of fuel and maintenance by reusing the AI-25 engine.
Biplane configurations are less efficient than monowings of the same total area due to interference between both lifting surfaces.
For crop-dusting applications in particular, @Harper points out the fact that the shorter span of biplanes is detrimental to effective spraying, by limiting the width of the spray system, which needs to end short of the wingtips. Otherwise the agent will get picked up by the wingtip vortexes and spread in unintended directions. 


On the other hand:


One advantage of biplanes is low roll inertia due to the shorter wings, which is mostly useful in dogfights and thus not highly-sought nowadays.
Another advantage of biplanes is the lower bending moment at the root of the individual wings, due to them being shorter. This allowed earlier designs to get into the air in spite of poor building materials and QA procedures; this solution was gradually abandoned as aircraft moved away from wood and fabric and towards aluminium alloys.
The lower span of biplanes might be useful in application that are span-limited, like modern airliners, which are limited by airport parking and runway restrictions. If you absolutely need to obtain more lift out of an airframe that is already at its maximum span, adding a second wing is not unreasonable.