It is a fact of life in Houston that sooner or later your house is going to grow mold on the paint. And sometimes on the brick.
I have tried several products that claim to handle this problem. By far the best of the lot is called Jomax. It is sold by the gallon at many stores in Houston, including Home Depots. One quart makes five gallons when bleach is added. Five gallons of prepared solution will treat 1,000 square feet of surface. It is one of the cheaper products for this job, and easy to use. It does not seem to hurt the plants and it has yet to discolor any of the nine different colors on my Queen Anne Painted Lady.
I have a tall house. I have found that the Ortho Tree and Shrub Spray-Ette is the best tool to apply the Jomax. The sprayer sends out a sharp stream of water that can easily reach about twenty feet high. I fill the plastic jar to the 36 liquid ounce mark with regular household bleach. I then fill the jar to the brim with Jomax. This makes the proper ratio for my house. I spray the plants with plain water (which you get when you use the Spray-Ette without the jar on) then add the jar with the Jomax and bleach apply the Jomax. I wet a section of the wood with the Jomax and let it sit for 3 to 4 minutes. I then unscrew and remove the jar and rinse the Jomax off with plain water. The mold just washes away. No need to scrub.
Be sure to wear old clothes and shoes and a hat and goggles. Bleach and eyes don't go together. Also, expect to repeat the process every 6 months or so if you want to keep all the mold away. You can go to once a year if your standards are more relaxed.
Give this product a try. It makes an unpleasant task more easy to finish.