Even if this were a fungus (most that appear on soil or mulch are harmless and merely decay organic matter), using a fungicide would not provide any benefit, so rest assured you don't need a chemical treatment option. This doesn't look fungal, though...it looks more like Nostoc, a type of cyanobacteria. (Despite sometimes having the common name of "blue-green algae," Nostoc is not actually algae.) If so, it can be very hard to control with any sort of treatment, but physical removal (scraping it off with a shovel and disposing of it) tends to work well.

Nostoc thrives in areas with persistent moisture and nutrient runoff (especially phosphorus). At nurseries, it's not uncommon, and tends to grow where sprinklers are used often and when fertilizer nutrients leach out of containers. In home landscapes, its presence might indicate a problem with over-irrigation (or poor drainage from compaction) or over-fertilization, though it's not necessarily a given. Where it came from is hard to say, but potentially pieces of a colony might have hitched a ride on nursery stock or blew into the area from some other location.

You can learn more about Nostoc in these pages:

• Nostoc: The mysterious green jelly on your lawn -- Michigan State University
• Nostoc Commune -- Ohio State University
• Nostoc -- Clemson Cooperative Extension

The Astilbe and Hellebores should be fine with regards to not being infected with anything, though the Hellebores might suffer if the soil does indeed have a drainage or wetness issue in that area. (Astilbe is more tolerant of damp soil, though it has its limits.)

Miri