If you are using electrospinning method to produce thin films, I will suggest you to keep the copper grid to the farthest point of deposition area and run the electrospinning for few seconds. You will get clear images of the nanofibres within the film.
You can always use FIB to extract a lamella of your substrate and then FIB again to thin the lamella further to around 100 nm, and once again FIB with Pt deposition to attach the lamella to a TEM grid. This is not a trivial task, so find a FIB/TEM expert to help you with this part.
If u are doing thin film... It's not straightforward...
After deposition when your thinfilm is ready... U can scratch out the film ...then disperse in solvent like water or ethanol... Sonicate it... Provided ur materials doesn't disolve in the solvent... Then drop it on copper grid....