Hi there, thank you for using ask an expert. I have been researching your question and unfortunately there is not a wood product that has yet been found to be immune to this fungus.  Cedar and cypress mulches are more resistant than other woods, with cypress being slightly better than cedar.  There is some research that shows that bark products versus wood products have a lower incidence of this fungus but over time as they break down they also get infected with the fungus.  A fungus requires moisture so our climate is perfect for growth during our rainy season.  Larger pieces of bark nuggets allow the rain to penetrate through to the soil more readily than smaller nuggets which will soak up more the water as it passes through and therefore are more susceptible to developing the fungus.  Studies show that the fungus is more of a problem during wet years and on the side of homes that are shaded and cooler.  Light colored paints not only show the spots but also can attract the release of the spore packets that the fungus releases by mimicking the lighter colored sky.  I do have some suggestions for you.  One is use a stone such as pea gravel or other type of rock as a mulch.  There are also shredded rubber mulches available made from recycled tires.  If you want to continue using an organic mulch get a bark product without any wood mixed into it (this will be tough as most have some wood mixed in).  Replenish the top 1- 1½ inches with fresh mulch every year.  If you have plants in the bed, evaluate the irrigation method.  You may want to change to emitters that water only at the base of the plants and not the entire bed, this would reduce the amount of moisture in the beds during our dry season and should reduce fungal population levels during the summer.  Finally, you could consider planting grass or some other ground cover if the site is too shady for grass.  Then there is the artificial turf option.....