You can extract microfossils and palynomorphs by treating the asphalt with kerosene for dilution , and then pass it through nylon mesh and pull the diluted asphalt or even crude oil by pipit and disseminate on slide, let the solution dry for overnight then use transmitted light microscopy to identify the particulate organic matter.
I don't know if this will work but might be worth a try. Use a soxhlet extractor with a suitable solvent such as petroleum ether. The residue in the thimble is collected and sieved with detergent. Mineral matter can then be removed by conventional palynological processing.
Suzanne Leroy just forwarded this question to me as I have had similar problems with many of my palynology samples. Jonah Chitolie helped me out massively earlier this year by sharing a few techniques. As he mentions above, solvents could be the way to go (I experimented using hexane, which worked after a fashion, but I still haven't got the method slick enough to process samples at a good speed). However, the method I have found most effective so far is Jonah's sieve/detergent approach. The way I currently do this is to wash the entire sample in a detergent at the begining of the process (I wash through 125microns to remove coarse clastic material immediately, then complete the wash by agitating the sample and draining it through 10microns to retain palynomorphs). The oil will be visible as a film on the surface of the sample and the idea is to wash until this is completely broken down. This can be done with a domestic detergent (such as washing up liquid) but it tends to foam a lot and the 10micron sieving can be very time consuming, especially if the sample is clay rich.