Make repairs to leaking pipes or rising damp. The trouble for people with asthma is that moulds colonise by releasing tiny seed-like spores into the air. When these are inhaled they can irritate the airways of those who are sensitive to them. Mowing the lawn or raking leaves is likely to release an abundance of spores into the air. Painted walls are preferable to wallpaper.
Wooden floors are preferable to carpets.
Replace old pillows and mattresses. Use barrier covers on pillows to protect against house-dust mites and also as a barrier to moisture from perspiration. Wash your dirty laundry regularly. A high-efficiency extractor fan can help to reduce humidity and direct steam outside when the bathroom is in use. Clean the bathroom regularly.