I have allergies to mites and mold; how do I avoid them?

Humidity Control. Both usually thrive in humid conditions (although some molds such as penicillium do not necessarily require high humidity), so using a dehumidifier may help and stopping any water leaks. For dust mites you should use bedding and pillow encasements and wash your sheets in hot water. A cochrane review also suggests that acaricides in conjunction with the above measures is best.
Dust mite allergy. Mites live mainly in cloth fiber areas, so in mattresses, rugs and upholstery. You can encase your mattress and pillow, aim for bare floors when you are able and lean toward leather and wood furniture. For mold, it's a matter of ensuring there are no damp areas in your home or workplace--leaks, mainly--plumbing. Or outdoor rainfall seepage, eg basement issues.