Separation

The foam should float, the paper should soak and sink...so would try a sample in a tub of water...

Then a multi-wire weir system, depending upon the volume that needs to be separated, that would determined settling time and size of tank required.

Thanks

You might want to heat the water to accelerate the process if necessary...

https://www.ncbi.nlm.nih.gov/pubmed/24461858

If you wish to retain the paper in a usable condition then electrostatic separation over a rotating drum as a head pulley on a conveyor. The two streams will separate and flow in a trajectory due to their attraction to the static charge and density. This method is used in sand mining to separate the various fractions into the constituent minerals.

Nothing has been said about particle size or quantities of material.

The biggest problem is likely to be whatever is holding the two together, about which nothing has been said.

• Paper will soften and may even decompose in water with a detergent added whereas <...polyurethane...> will not.
• <...polyurethane...> will probably decompose or even dissolve in dilute hydrochloric acid, however the strength of the acid may affect the <...paper...>.

Is it too soon for some "bucket chemistry" testing?